We would not refer to someone who is from the Caribbean, for example, as "African". We would say either "He's Black" or "He's from Jamaica".
While I realize it may be considered offensive to some in American culture, in Canada this is the norm. If the person is not "Black" but might be say, Indian we would say "Brown" or the ethnicity if known (ie. "He's this Sri Lankan guy...")
I've had conversations with Black-Canadians who are actually *offended* to be called "African" because their ethnicity is more entrenched with the Caribbean culture than African culture. That being said, we also have *African* immigrants, and those people, while Black would also be African (ie. "He's a Black guy, he's from Ghana...")