graybeard vs adult male

graybeard and adult male both are nouns.

Word	Noun	Adjective	Verb	Adverb
graybeard	Yes	No	No	No
adult male	Yes	No	No	No

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

Other hypernyms of graybeard include man, golden ager, old person, oldster, senior citizen.

graybeard (noun)	adult male (noun)
a man who is very old	an adult person who is male (as opposed to a woman)