Black American vs Afro-American

Black American and Afro-American both are nouns.

Word	Noun	Adjective	Verb	Adverb
Black American	Yes	No	No	No
Afro-American	Yes	Yes	No	No

As nouns, Black American and Afro-American are synonyms defined as:

Black American and Afro-American: an American whose ancestors were born in Africa

Other synonyms of Black American include African American.

Black American (noun)	Afro-American (noun)
an American whose ancestors were born in Africa	an American whose ancestors were born in Africa

Black American (adjective)	Afro-American (adjective)
	pertaining to or characteristic of Americans of African ancestry