I’m not sure who you are asking, but I think of myself as African-American, which to me means a Black person of African descent in the US for several generations, usually via slavery . This is different from my husband, who is Caribbean- American, born in Jamaica, his children the first in his family to be born here.
The perspective is more different than some people appreciate.
I also consider myself from NYC, where I grew up, but I have now been in California for about half of my life.
Please accept that this answer comes from someone who never had the benefit of a college/university education and certainly has minimal grasp of UK constitutional law…
…Neither the Isle of Man , nor the Channel Islands are part of the UK. They do not elect Members of Parliament and have their own legislatures. Their technical designation are as “Crown Dependencies”. This is similar, but different, to the UK’s “Overseas Territories” (like Gibraltar, Bermuda and Pitcairn). The legislatures of the Dependencies are responsible for all internal home affairs - taxation, justice, immigration, etc - but the UK government (on behalf of the Crown) has responsibility for defence and foreign affairs.
There is a similar sort of regional affinity in the UK. If I was visiting a foreign country and I was asked where I was from, I would generally reply that I’m northwest England. I have some pride in the region - it’s history, geography, culture, food, etc.
I don’t think that’s particularly unusual in Europe. I guess that, depending on the circumstances, Barca may well describe herself as being Spanish and Catalan. Someone else might self describe as Italian and Sicilian. And so on.
By the by, recent surveys in England have shown that, generally speaking, people who voted for Brexit self-defined as English, whilst people who voted to remain in the EU generally self-described as British. It’s the sort of subject that, if we discuss it further here, we will quickly cross into political and cultural matters such as I suspect are very similar to those being discussed in America over recent days/weeks.
Puerto Rico not being a US state but being a US place anyway, is similar, in at least a vague superficial way, to the dependencies and overseas territories of the UK.