mountain man vs adult male

mountain man and adult male both are nouns.

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

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

Other hypernyms of mountain man include man, pioneer.

mountain man (noun)	adult male (noun)
a man who lives on the frontier	an adult person who is male (as opposed to a woman)