The transatlantic OP has blundered into a nest of more or less friendly hornets.
A lot to say - I won't now.
Even people not as far away as the OP, namely in Europe, are quite confused about it, and this goes for people who ought to know like press reporters.
But then many Europeans are quite confused about Canada. Like it's in America isn't it? - but hold on, there is something or other funny about it. But perhaps there is about Texas too.
Basically Continentals call the whole lot England, Angleterre, Inghilterra, Engeland, etc. It leads to descriptions which to the British sound distinctly odd, like the English Army, English Navy or English Parliament or Government - inexistent entities.
Then to complicate matters as well as the places already mentioned in the thread there are what are called 'Crown Dependencies' (the Channel Islands and Isle of Man) which are not part of the UK nor represented in Parliament, not colonies, self-governing yet not totally independent, recognise the Queen whose head is on their coinage and stamps.
What is really behind all the complication is that Great Britain has a continuity of history without the kind of breaks represented by the American or French Revolutions. Thus the formal feudal system and model of sovereignty was never totally torn up to start with some new founding document or Constitution like most Continental countries under the influence more or less of the French Revolution. In practice it adapts while respecting some archaic forms and, very broad-brushing, the country has little, indeed less than nothing, to envy others in terms of substantial modernity most, not all, of us have tended always to think.
The British Constitution only began not before the Blair governments, i,e, practically this century, to change from something that had hardly changed since 1911 and would have been quite recognisable and familiar to Victorians. Propelling changes were: nationalist or devolutionist forces and voices, interests, sentiments etc.; the desire of Blair and Blairites to look modern; the redimensioning of sovereignty and adaptations implied by membership of the European Union, which in particular works with a different system and concept of law than the English. Of course once you change one part you find you can't stop another, perhaps unforeseen, changing.
The US masses probably only got their first awareness of any of all this when people were surprised that on the Megrahi (Lockerbie, Libyan) scandal they found they were not dealing with the UK Government in London but with a (fruitcake of a) Scottish Justice Minister and 'Government'. Do not be deceived: firstly this had nothing to do with any of these changes, Scotland has always had a different Law and legal system (more influenced by Roman Law) than England; secondly if the UK government said it has no influence that is not because of the independent legal system but rather because different political parties (Labour and Scottish National Party) controlled the different parts and they hate and try to diddle each other.