white man vs adult male

white man and adult male both are nouns.

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

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

Other hypernyms of white man include Caucasian, White, White person, man.

white man (noun)	adult male (noun)
a man who is White	an adult person who is male (as opposed to a woman)