If they're black and British and you're describing their nationality you'd say they were British.
Not only do many of them not see themselves as such because they're born here, and their parents and grandparents might be British and/or born here (my son is mixed, his grandfather on his mothers side was Nigerian and British and born here; he is third generation British by some measure - his mother was born in Nigeria, but holds British citizenship due to her father; if he decides to consider himself African or Nigerian - he has a Nigerian citizenship - that's up to him, but he's born here, to a mother with a British citizenship, and has never set foot in any part of Africa), but another significant proportion of black people here consider themselves Caribbean rather than African, because their ancestry goes back many generations in the Caribbean, and that's where they or their recent ancestors immigrated from.
Here, "forcing" a categorization of "African" on someone will be seen by at least some people as implying they're immigrants, and even when that is actually the case, having the label forced on you is often a prelude to racist sentiments.
The other comment from hot_gil sums it up well,
"""
I promise it's not because we think of people outside the US as American. When I was a kid in the 2000s, we were told never to say "black" and to say "African-American" instead. There was no PC term in the US to refer to black people who are not American. This has started to change lately, but it's still iffy.
"""
There has been very vocal pressure to understand "lived experiences". This, to me, qualifies exactly as that and is purely a misinterpretation of the author's intent.
Hence for many people it becomes important to de-emphasize "another location" in how they identify that might imply they somehow don't belong. While for others holding on to a culture that is often a lot closer matters.
And so the discourse around labels is very different.
As an aside, I once was considering trying to spend some working years in Scandinavia but read that it was likely I would always be kept at an arm's length by the locals since I was non native, regardless of my fluency in the language. As an American, I found it odd considering how heterogenous my social circle was. Maybe totally false or not applicable to urban centers, but I read it from various sources, and it was persuasive enough for me to switch focus to mainland Europe.
To the point there are books about how to befriend us [1]. There's also this meme[2] of Finns always spacing out at bus stops to avoid invading each other's personal space, for example, but while Finland is perhaps on one extreme of that, Scandinavia as well is close. Denmark maybe a little bit less and in Norway and Sweden.
The way around that tends to be shared activities. E.g. joining a class, going out with colleagues, or joining various groups, or getting drunk, where you then have a socially sanctioned reason for talking to people, and people build from that. People who are used to being able to start friendships with just random encounters will often find that frustrating and hard to navigate and wonder why they're blanked or ignored or actively rebuffed when trying to be friendly - it's not you, or where you're from (most of the time), it's that talking to a stranger makes a lot of people instantly wonder what fresh hell this is. It's not that random encounters etc. never lead anywhere in Scandinavia, but it's rarer. If you move to any of the Nordic countries and don't know or pick on that you will have a bad time. Unless you're a massive introvert - then it's awesome.
For someone who is used to expecting American levels of just randomly talking to people (having been on the receiving ends of that many times when visiting the US: I could never get used to that...), getting used to that might be hard, and basically the further South you go in Europe the less you deal with that.
[1] https://www.thesocialguidebook.no/blogs/norwegian-culture I bought the first one of this guys books as a joke for my non-Norwegian girlfriend, and it gets things mostly right, I think.
[2] https://www.reddit.com/r/Finland/comments/1494mm/how_to_wait...
If you called my Black friends "African American" they would be pretty close to punching you in the face.
Why wouldn't it be racist to assume Black people are African.
The instant escalation to violence seems like part of the problem generally in today's society, which extends to non racial topics like politics, gender fluidity, etc.
A more appropriate reponse would be something like, "Why do you think I'm American?" A simple question like that would likely be sufficient to get the original speaker to think abkut and reorient their world view, and there was good-faith discussion the entire way.
Black American, same way.
"African-" implies you were born in Africa, "-American" imples you then immigrated to America.
Elon Musk is an African-American.
13% of the US population are Black Americans.
Elon Musk is not considered African-American according to the popular usage of the term as he is of European descent despite being born in South Africa.
My ex would probably grudgingly accept black British, but would describe herself as black, Nigerian, or African, despite also having British citizenship.
If you're considering how to describe someone who is present, then presumably you have a good reason and can explain the reason and ask what they prefer. If you're describing someone by appearance, 'black' is the safest most places in the UK unless you already know what they prefer.
"Nobody" uses "African British".