greybeard vs adult male

greybeard and adult male both are nouns.

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

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

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

greybeard (noun)	adult male (noun)
a stoneware drinking jug with a long neck; decorated with a caricature of Cardinal Bellarmine (17th century)	an adult person who is male (as opposed to a woman)
a man who is very old