Black man vs adult male

Black man and adult male both are nouns.

Word	Noun	Adjective	Verb	Adverb
Black man	Yes	No	No	No
adult male	Yes	No	No	No

As nouns, adult male is a hypernym of Black man; that is, adult male is a word with a broader meaning than Black man:

Other hypernyms of Black man include African-American, Black, Negro, Negroid, man, Black person, blackamoor.

Black man (noun)	adult male (noun)
a man who is Black	an adult person who is male (as opposed to a woman)