Is there a political term for a strong (democratic) state that has much influence in contrast to a weak one?

Question

Some political parties (ie economic liberalism) want a "weak" state that has less influence, other seek a strong one.

Is there a term that describes a (democratic) state that is a strong one?

Answer 1

A popular political direction which favors a big government dedicated to upholding democratic ideals like liberty and equality is social democracy. The systems of many European states are often described that way. An even stronger form which hasn't seen much use in the real world yet is democratic socialism.

The main difference between these two ideologies is that social-democrats consider free markets a tool which can be used to solve many (but not all) problems, while democratic socialists consider a state-controlled planned economy to be inherently superior to a free market economy. Both differ from pure socialism in that they want to bring and govern their respective systems in a democratic manner and not enforced through an autocratic government.

Answer 2

Misread the question (thought it was about what is covered in weak government political theories). But thought I'd outline the Small Government models (As opposed to Big Government, which @Philip covered). As asked "Big Government" is the term for a Government that is stronger and often more centralized. Small Government encompasses a lot of different ideas characterized by a weak central government with a more powerful regional government. These terms are more common to governments with Strong Federalism (i.e. a bunch of small nations decide to collectively cede power to form a large one) and tend to form around what the highest level of government can do with respect to the law and the lower levels of government. Generally opponents of Big Government believe that the Government is not the solver of all societal problems and that it might fall to a lower level of government authority OR a private cooperation that can make innovative changes faster than the government can. Proponents of Big Government believe that the higher level of government can leverage more resources than the lower level and should act in situations where the lower level government is too weak to act (either the will of the people is preventing important social changes or regulations on big industries). These are lose definitions and are not all favored by people (Big Government is a bit more pejorative as it gives the idea of a soulless giant monster ala Big Industry, Big Medicine, Big Oil) so the term is rarely used by people who support it.

In the United States, this system of Government is called a Jeffersonian Democracy, which favors a weak centralized government (without writing tons, a Jeffersonian believes the Local Government should have more control over an individual by law as they are easier for the individual to fight) and as the scope of authority rises in a federal system, the government deals less and less with the individual and more and more with lower governments. This is mostly academic. The Crux of all U.S. Politics is Jeffersonian Democracy (American Conservatism) vs. Jeffersonian Democracy combined with Jacksonian Democracy (basically, more government roles should be decided by popular vote. This belief is such an integral part of the Democrat party, that until recently, they would have a big "holiday" celebrating the two individuals with a fund raising dinner. These are no longer popular as Jefferson was a slave owner and Jackson committed illegal genocide against Native Americans. Still their ideas on government are popular...).

Constitutional Republics (especially those that used the U.S. Constitution in part or wholesale as a Constitution model) are governments where the highest law of the land are laws that restrict the government (in the U.S. the government is the only legal entity that can commit illegal offenses against the constitution). All democracies in the world are Constitutional save for the UK and New Zealand, which are Parliamentary (the legislature makes the ultimate law) (Australia may qualify as they have Constitutional Law, but not defined by one document), though the level of restrictions may vary between country.

Classical Liberalism (in the European sense) are the ideas that the American Founding Fathers founded the United States on. NeoLiberalism is an offshoot of that, which tends to favor Economically Liberal (European Sense. They are Conservative in the United States) and Socially Progressive policies.

Libertarianism (especially in the United States) is the idea that a government should be concerned about protecting the rights of an individual from abuse by other individuals (or government) but the range of individual agreements is set by the two individuals (i.e. there is a contract between two individuals that includes a morally offensive act. It is valid if both parties understand the terms of the agreement and willfully accept them. The government should not interfere unless the terms not fairly represented. I.E. The government should not interfere in the sale of an immoral substance unless the price for transaction was not payed by one of the parties. The Government has no right in preempting the contract by making the sale of the substance illegal.) (American Libertarians tend to be closer to political conservatives, but they greatly divide on military spending).

Anarchy abolishes all government and makes the enforcement of individual rights the duty of other individuals (also a pure/direct democracy does this. Basically "Democracy is two wolves and a sheep deciding what's for lunch.").

Apologies for the America-centric nature of this and switching between terms (I tried to explain which terms are related to which geographic area). American Politics have historically been between Big Government (The Federal Government) and Small Government (States and/or local level), so the ideas encompass their own terms a lot. In fact, a 2013 Pew Research Poll found that 54% of Americans believe their government does too many things as is.

As with all political terms, this one tends to get defined under a lot of different ways. Just how much government is too much verses what to cut to shrink government is not agreed upon among small government circles. Often it is seen as a good thing to fight the government on any grabs for more power as it is harder to take it back once government does get it.