gay man vs adult male

gay man and adult male both are nouns.

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

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

Other hypernyms of gay man include gay, homo, homophile, homosexual, man.

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