schoolmarm vs adult female

schoolmarm and adult female both are nouns.

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

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

Other hypernyms of schoolmarm include school teacher, schoolteacher, woman.

schoolmarm (noun)	adult female (noun)
a woman schoolteacher (especially one regarded as strict)	an adult female person (as opposed to a man)