male monarch vs adult male

male monarch and adult male both are nouns.

Word	Noun	Adjective	Verb	Adverb
male monarch	Yes	No	No	No
adult male	Yes	No	No	No

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

Other hypernyms of male monarch include man, crowned head, monarch, sovereign.

male monarch (noun)	adult male (noun)
a male sovereign; ruler of a kingdom	an adult person who is male (as opposed to a woman)