The United Kingdom's full name is the United Kingdom of Great Britain and Northern Ireland. Thus, technically, referring to the UK as "Great Britain" excludes Northern Ireland.
Great Britain is used to formally refer to the UK (including Northern Ireland) in a number of international associations. For example:
The term might not be technically correct, but its use to refer to the UK is certainly not limited to US politicians.
Short Answer - GB is more than the island
When politicians – whether in the US or not – and people in general use the term Great Britain they are normally referring to all of the hundreds of British Islands over which the British Queen rules, not just to the largest island which is named Great Britain. When used in this political, rather than strictly geographical, sense the term includes Northern Ireland and all the other islands in the UK plus Mann and the British Channel Islands.
Long story short 1000 years ago two countries each had lots of small islands and also shared one nearby big island named Great Britain. About 950 years ago a king whose kingdom included another set of five small islands off the French coast conquered one of those countries. About 420 years ago a later king inherited the thrones of both countries and of the five original islands. That king wanted the parliaments of the two countries to agree to combine in a united kingdom to be called Great Britain. The parliaments refused to combine but the king told them he would still use the title King of Great Britain. The parliaments told the king that he couldn’t do that but the king and his successors kept using the title nonetheless and the rest, as they say, is history. Parliament has changed its formal title several times over the past 320 years as a result of amalgamation and disaggregation, even calling itself the Parliament of Great Britain at one stage, but through all that Great Britain has remained as the everyday term for the kingdom which contains the island of that name however many other islands it may, at any time, also contain.
GB is more inclusive Mann and the British Channel Islands are not part of the kingdom but have the same king who rules as Lord of Man and Duke of Normandy respectively. Manxmen and Channel Islanders are no less British citizens than the inhabitants of the UK and unless a speaker is for some reason specifically referring to the UK only, the inclusive term to use is Great Britain which, as a less precise term, can be used either to refer to the UK or to refer to all the British Islands. Why would a US politician wish to use a term – UK – which excludes the island of Jersey which gave its name to the 3rd State of the USA?
When used in a political sense the term Great Britain is not intended to exclude Northern Ireland any more than it is intended to exclude for example Portsea, Wight, Anglesea, Sheppey, Canvey, or Lewis and Harris. When you have over 100 inhabited islands no collective name can mention them all.
Great Britain is Grande Bretagne in French and both languages use the abbreviation GB. Great Britain also has a convenient adjectival form - British - and a noun for the people who live there - Britons (both words are Britannique in French). You can’t (or at least nobody does) say Uker or UKon and in any event using UK would exclude 6 islands and so would be inaccurate unless the speaker intends to exclude those six islands.
But doesn’t the very term “Great Britain” exclude by definition any part of “Little Britain” = the island of Ireland?
Some people who accept that a term can be used in a political sense which is wider than its geographical sense nevertheless argue that Great Britain should not be used as a term for anything which includes any part of the island of Ireland. They reason that because one classical geographer referred to Ireland as Little Britain, it is intrinsic in the idea of Great Britain that it does not include the island called Little Britain (whatever other even smaller islands might be lumped in with it). The flaw in this reasoning is that although the classical writer Claudius Ptolemy referred to the islands in general as Britannia, and did indeed name the largest great Britain (megale Bretannia) and the second largest, little Britain (mikra Brettania) in his work, Almagest (147–148 AD), in his later work Geography (c. 150 AD), he gave these islands the names Alwion and Iwernia and used Britannia to refer only to the island group. His writings were not known in Europe during most of the Middle Ages. During the Middle Ages Little Britain was the name given to Brittany in France to which many Britons migrated in the 4th and 5th Centuries and Great Britain was given that name because it was where those Britons came from. 16th Century cartographers followed Ptolemy in referring to the whole archipelago as the Britannic Islands but never referred to Ireland as Little Britain. By that time the term Great Britain/Grande Bretagne had already been in use for a millennium being understood as meaning where the people in Brittany/Bretagne came from. The idea of Ireland being Little Britain was never adopted - Little Britain always meant Brittany.
A point worthy of note, by way of background, is the difference between the British Isles and the British Islands.
The geographical term British Isles refers to the whole archipelago, that is the two largest islands, Great Britain and Ireland, the smaller islands on their insular shelves, and the Isle of Man which is equidistant between them.
The political term British Islands (defined in the Interpretation Acts 1889 to 1978 but used in international treaties before then) refers to those islands in, or in the vicinity of, the British Isles over which the Queen reigns. There is a large overlap between the two but British Islands does not include the Republic of Ireland whose territory occupies the majority of the island of Ireland. On the other hand British Islands does include the British Channel Islands which are on the other side of the English Channel from the island of Great Britain and so are not part of the British Isles.
There is a helpful Venn diagram here https://commons.wikimedia.org/wiki/File:British_Isles_Euler_diagram_15.svg
The British Islands consist of four separate realms which the Queen rules over:
- The United Kingdom of Great Britain and Northern Ireland
- The Isle of Man (in respect of which she is Lord of Mann)
- The Bailiwick of Guernsey (in respect of which she is Duke of Normandy)
- The Bailiwick of Jersey (in respect of which she is Duke of Normandy)
Only (1) is a state in international law, as international law has developed since the Peace of Westphalia. Following the Balfour Conference and Declaration in 1926 His/Her Brittanic Majesty no longer enters into international treaties in his/her own name and instead (1) enters into international treaties on behalf of itself and (depending on the subject matter) also on behalf of some or all of 2, 3 and 4.
Use of “Great Britain” as a political term
For a period of slightly less than 100 years (from 1707 to 1801) there existed a kingdom whose parliament was called the Parliament of Great Britain. From this fact some people deduce either that Great Britain has no meaning (other than as a geographical term for the island) before or after that 94 year period or else that, if it does have any political meaning after 1801, it is the name of some kind of political sub-set of the expanded state.
But in fact Great Britain has been in widespread and continuous use as the usual word for the British Islands for over 400 years and, since the meaning of a word is ultimately determined by usage, I would argue that it is not only common but is actually correct to use Great Britain in this way. King Kames I of England (IV of Scotland) appears to have been the first to use Great Britain as a political description.
Queen Elizabeth I of England never married and, upon her death in 1603, the King of Scotland, James VI inherited the thrones of England (and Ireland) as James I, thereby uniting the Crowns.
James I wanted to unite the Kingdom of England and the Kingdom of Scotland in a single kingdom to be called Great Britain, the name of the largest island in his proposed combined kingdom. The Parliaments of England and Scotland refused to unite and told the King that he could not use the title King of Great Britain but he used it nonetheless and the name Great Britain has been used ever since.
James I used Great Britain when it was not the official name of either the Kingdom of England or the Kingdom of Scotland but a century later the Acts of Union 1707 actually combined the Kingdom of Scotland and the Kingdom of England into one, officially named the Kingdom of Great Britain. A century later, in 1801, the parliaments of the Kingdom of Great Britain and the Kingdom of Ireland voted to unite as the United Kingdon of Great Britain and Ireland. That is a nice formal name - the longest country name in the world, apparently - but it is not designed for everyday use.
In hindsight it seems obvious that use of Great Britain as the name of the combined kingdom would continue. When James I first used the name he used it for a proposed combined kingdom which contained not only the island of Great Britain but a great many other smaller islands as well so why should the addition of further islands make any difference to its suitability? The term had originally been used against the wishes of parliament so why should a further parliamentary name change make any difference especially since parliament's new name was too long for everyday use?
It was not just ordinary people but government officials also who continued to use Great Britain. In 19th Century and early 20th Century treaties Great Britain is typically in the title of the treaty as the name of the state without the words United Kingdom of Great Britain and Ireland appearing at all - see here, here, here, here, here and here. Where the words United Kingdon of Great Britain and Ireland do appear in a treaty that is usually because the treaty has been entered into by the monarch herself and the words appear only as part of her title (along with Empress of India) - see here, here and here.
Even where United Kingdom of Great Britain and Ireland is indicated as the contracting party in a treaty, when the signed treaty is presented to parliament in a command paper the short title assigned will often be Treaty between Great Britain and... as in this example.
After the 1926 Balfour Conference it became progressively more common for treaties to be entered into in the name of the UK and that is now the consistent practice.
The Report from the 1926 Balfour Conference is of particular interest as evidence of how the term Great Britain was being used in the first half of the 20th Century. Being a document carefully drafted by someone very aware of the different sensitivities of all those attending, its use of language is deliberate and not accidental. It shows that Great Britain is the usual short name for the United Kingdom/the British Islands with Britain having the same meaning and being occasionally used for the purposes of elegant variation.
II. STATUS OF GREAT BRITAIN AND THE DOMINIONS. ...There is, however, one most important element in it which, from a strictly constitutional point of view, has now, as regards all vital matters, reached its full development — we refer to the group of selfgoverning communities composed of Great Britain and the Dominions... Equality of status, so far as Britain and the Dominions are concerned, is thus the root principle governing our Inter-Imperial Relations.
IV.RELATIONS BETWEEN THE VARIOUS PARTS OF THE BRITISH EMPIRE. ...The representatives of Great Britain readily recognised that the existing procedure [regarding one aspect of a Governor General's role] might be open to criticism and accepted the proposed change in principle in relation to any of the Dominions which desired it.
Usage of "Great Britain" today
Today, in most of Britain, I would say that Britain or Great Britain are still the usual words in ordinary usage. UK is used when a precise word is needed which excludes those British Islands which are outside the UK. For example someone in the British Channel islands would not say British Parliament but rather UK Parliament because they are British too and it is not their parliament.
People on the island of Great Britain rarely refer to the island by name and when the say Great Britain they are nearly always referring to the state (or to all the British Islands) rather than the island specifically. People in Northern Ireland, however, may more frequently refer to the island of Great Britain by name (e.g. “he is flying over from GB”) and for clarity may be more likely to choose another word such as UK when referring to the state.
In French also Grande Bretagne is used as the name of the state as well as the name of the island. If you look at any written material in French today you will see Grande Bretagne being used as the name of the whole state across the channel. For example, an article about France's national debt, comparing it to that of other counties, on the French government website says:
L’endettement de la France n’est toutefois pas une situation isolée. De grands pays comme la Grande-Bretagne, les États-Unis ou le Japon font également face à des dettes publiques importantes qui témoignent de l’impact mondial des crises économiques successives.
The official website of the British Embassy in Paris is headed:
L'ambassade de Grande-Bretagne à Paris
GB is, of course, the two character international country code for the kingdom and/or the wider British Islands. GB can stand for both Grande Bretagne and Great Britain (whereas United Kingdom and Royaume Uni have different initial letters).
The curious case of the car stickers
The International Vehicle Registration Code was GB, from 1910 up until 2021, with GBA then used for Alderney, GBG for Guernsey, GBJ for Jersey, and GBM for the Isle of Man. During Brexit negotiations at one stage the EU insisted that cars driving over the border to the republic of Ireland would have to display a GB sticker. Irish Nationalist politicians in Northern Ireland said that GB to them was not inclusive of Northern Ireland and in response to those concerns the UK government floated the idea that the code could be changed from GB to UK to make it more "inclusive" but people in the Bailiwicks of Guernsey and Jersey then pointed out that changing from GB to UK would actually make it less inclusive because UK was not appropriate for those British Islands which are not in the UK. In the end the EU backed down and did not insist on stickers being displayed on vehicles going to the republic from the UK but by that time the UK government was committed to changing from GB to UK and that change went ahead BUT, at the last minute, it was conceded that GBA could stay for Alderney, GBG for Guernsey, GBJ for Jersey, and GBM for the Isle of Man.
So, why do US politicians use Great Britain to refer to the UK?
Because so does everyone else. Great Britain actually has four meanings like four concentric circles.
As a geographical term - The island of Great Britain.
As a geographical term - (1) plus plus the smaller islands on the insular shelf of Great Britain.
As a political term - The United Kingdom of Great Britain and Northern Ireland.
As a political term - (3) plus all of the other British Islands.
Perhaps they are following the lead of their counterparts in the United Kingdom, who frequently speak of "Britain" in contexts where it seems to stand for the entire kingdom. Examples:
the leader of the opposition: "Too many people in Britain today..." (https://keirstarmer.com/plans/a-just-society/)
the prime minister: "...we will invest in Britain’s people..." (https://www.conservatives.com/our-plan/introduction-from-boris-johnson)
Because "The United Kingdom of Great Britain and Northern Ireland" is simply too long for easy speech. Same reason the US is seldom referred to as "The United States of America", Mexico as "Los Estados Unidos Mexicanos", Canada as "The Dominion of Canada", and so on. FTM, I would guess that just "Britain" is more common than "Great Britain".
FTM, why do the British talk about Queen Elizabeth, and not "Elizabeth II, by the Grace of God, of the United Kingdom of Great Britain and Northern Ireland and of her other realms and territories Queen, Head of the Commonwealth, Defender of the Faith"?
Same reason basically that so many people use "America" or "United States" instead of "United States of America": it's short and easy to say.
Brazilians tend to be specifically pissed off at referring to the USA as "United States" as that's what they call their own country...
Or how many people refer to the Kingdom of the Netherlands and overseas territories (yes, that would be the full name if anyone used it) as "the Netherlands" (no, referring to it as "Holland" is dead wrong, but done a lot too).
And then there is referring to the People's Republic of China as simply "China" which is far worse as it denies the existence of the Republic of China on Taiwan. Then there is the Republic of Korea, often referred to simply as "Korea" despite there also being the Democratic People's Republic of Korea.
Used to be there were the German Federal Republic (usually just called "Germany") and the German Democratic Republic (usually just called "East Germany").
And I'm sure there are many other instances where the commonly used name for a country is an abbreviation of the full name.