Typically, African-American means black AND, unintuitively, American for generations IME. Maybe it shouldn't mean that but that's kind of assumed where I live at least. For first or second generation Americans you might use the country (eg Nigerian-American). For other races from Africa you'd also rarely hear them referred to as African American.

Of course, part of the issue here is that there isn't really a good shorthand term for "the group of American Black people of diverse African origin whose cultures were oppressed and destroyed by the white majority for centuries, leading to a mélange culture intentionally constructed out of the remaining scraps".

But "Caucasian" is (was?) used for people who for many generations weren't anywhere near Caucasus Mountains.

It's a bit weird from the outside tho cause if you're a white south-african and you hear the phrase used in America you'd be like "oh, I should refer to myself as an African-American" although unlike Americans, people generally only refer to themselves as being from the place once they have citizenship (and would therefore have learnt the intricacies of the American phrase) and even then many people choose not to.

American: "I'm Irish" Me: "No, you're not"