I think Mrs. May wants another box to be added to that diagram. Whether she achieves it or not is debatable. She wants to have a free trade agreement (like Canada) that includes goods AND services (generally FTA's cover just goods) while providing the freedom for the UK to negotiate its own free trade agreements.
Apparently CETA covers 98% of tariff areas - so it's pretty comprehensive on goods (and the Canadians don't have to pay or accept the four freedoms).
As to "regulatory alignment", it's worth remembering that anyone who exports goods or services to another country has to abide by the rules of that other country and vice versa for imports.
And even within the EU countries have some regulatory divergence. For example, power plugs in the EU and the UK and Ireland are different.
Ireland and Northern Ireland also already share common regulatory alignment (i.e. different from the rest of the UK) in a few areas, for example on phyto-sanitary matters, so there are already special arrangements in a number of areas for Northern Ireland.
The question is to what degree and how the UK implements EU regulations in a post-Brexit world, and what organizations are used to implement those regulations. Either way, it isn't tough to see the UK implementing some regulatory framework that retains regulatory equivalence.
Even with WTO terms (the so called "hard Brexit"), the economic costs or tariffs are not that great and would be discounted before the exit day by revaluation of the currency. In other words for the population as a whole there really is no "cliff edge". (Doesn't mean there aren't those who would suffer significantly - but there would be others who benefit significantly).
Approximately 28% of UK GDP is from exports or which EU exports amount to 43% or 12% of the total. It follows that even with EU tariffs at WTO rates (average 4%) the overall impact is minimal on the economy as a whole, and the UK would have the option of reducing tariffs on imported food, clothing and footwear. Imported vehicles from outside the EU might also have reduced tariffs by up to 10%.
The problem comes from non-tariff barriers, and here some agreement is needed between the EU and UK in order to avoid craziness on the exit day if there was no deal. It seems almost inconceivable that some accommodation on aviation etc. would not be found but in areas that are more commercially sensitive there could be an impact.
Since the development of the WTO the economic benefits of the EU are questionable (there is always that net payment of 12 billion to outweigh any advantages), and the main reason to stay is political and social.