old man vs adult male

old man and adult male both are nouns.

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

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

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

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

Other hypernyms of old man include man.

old man (noun)	adult male (noun)
an informal term for your father	an adult person who is male (as opposed to a woman)
a man who is very old
a familiar term of address for a man
(slang) boss
aromatic herb of temperate Eurasia and North Africa having a bitter taste used in making the liqueur absinthe