he-man vs adult male

he-man and adult male both are nouns.

Word	Noun	Adjective	Verb	Adverb
he-man	Yes	No	No	No
adult male	Yes	No	No	No

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

Other hypernyms of he-man include man.

he-man (noun)	adult male (noun)
a man who is virile and sexually active	an adult person who is male (as opposed to a woman)