Having lived in the UK, I can tell you that it really is that complicated. In fact, it is even worse. They didn’t even get into the status of the Isle of Mann, or the Channel Islands.
And then there’s the Falklands, another part of the UK, even though they are just off the southern tip of South America. Fun fact: did you know that a major naval battle of WWI was fought in the Falklands, even though they are far away from Europe?