tribal sheikh vs adult male

tribal sheikh and adult male both are nouns.

Word	Noun	Adjective	Verb	Adverb
tribal sheikh	Yes	No	No	No
adult male	Yes	No	No	No

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

Other hypernyms of tribal sheikh include man, ruler, swayer.

tribal sheikh (noun)	adult male (noun)
the leader of an Arab village or family	an adult person who is male (as opposed to a woman)