In the US, the vast majority of black people have descended from the enslaved Americans who have been in the US for hundreds of years. When people say "black culture" that's what they are referring to. Not that recent immigrants from Jamaica and Nigeria are from the same culture.
There's the further concept that due to systemic racism, Jamaican and Nigerian culture will blend into the larger black culture than the larger US culture. And the Nigerian and the Jamaican will experience a similar American experience, very different from what an Irish or German white person would.
When an American says "black", they often mean "African American". The reasons why one would use one word over the other is usually more about social conventions between synonyms and less about trying to describe different ideas.
It's really self-centered when we use "black" to mean "African American". It's strange when it goes the other way. You'll hear some Americans call Idris Elba an African-American.
When I say "Black", I mean "Black". If I want to single out Americans, I say "Black Americans."
I'm all for dropping the term African American, unless it's referring to a recent immigrant. It's a misnomer from the past, that for some reason people consider PC.
There's the further concept that due to systemic racism, Jamaican and Nigerian culture will blend into the larger black culture than the larger US culture. And the Nigerian and the Jamaican will experience a similar American experience, very different from what an Irish or German white person would.