tribal sheik vs adult male

tribal sheik and adult male both are nouns.

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

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

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

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