cleaning man vs adult male

cleaning man and adult male both are nouns.

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

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

Other hypernyms of cleaning man include cleaner, man.

cleaning man (noun)	adult male (noun)
a human female employed to do housework	an adult person who is male (as opposed to a woman)