I think it’s all a matter of perspective and opinion – that of the individual being asked their nationality/background. Sometimes it’s better just to ask that individual (when in a group) what they prefer themselves to be called, and cite all the names “black”, “African American”, etc. I have heard from many black friends and associates in America who have all kinds of preferences, and some are quite offended when they hear the other preference being uttered.
It is understandably a touchy subject for all considering this country’s history of racism (ie we tread lightly now). Kind of like asking someone from an American tribe if they prefer “native” to “Indian” and so on.