headmaster vs adult male

headmaster and adult male both are nouns.

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

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

Other hypernyms of headmaster include man, head, head teacher, principal, school principal.

headmaster (noun)	adult male (noun)
presiding officer of a school	an adult person who is male (as opposed to a woman)