headmistress vs adult female

headmistress and adult female both are nouns.

Word	Noun	Adjective	Verb	Adverb
headmistress	Yes	No	No	No
adult female	Yes	No	No	No

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

Other hypernyms of headmistress include head, head teacher, principal, school principal, woman.

headmistress (noun)	adult female (noun)
a woman headmaster	an adult female person (as opposed to a man)