But yes, you are correct. Anyone refering to 'Britain' probably means the UK, in the same way that non north American people refering to 'football' are referring to association football, and not, for example, the Eton wall game.
(, Wed 23 Jun 2021, 15:37, Reply)
The one made up of 50 'states' (NB, not all states, Kentucky is a commonwealth, etc,) plus a number of 'territories,' any of which could be argued is a nation.
And that's not even considering the various native American 'nations' which exist within the USA.
(, Wed 23 Jun 2021, 17:03, Reply)