old boy vs adult male

old boy and adult male both are nouns.

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

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

Other hypernyms of old boy include man.

old boy (noun)	adult male (noun)
a vivacious elderly man	an adult person who is male (as opposed to a woman)
a former male pupil of a school
a familiar term of address for a man