schoolma'am vs adult female

schoolma'am and adult female both are nouns.

Word	Noun	Adjective	Verb	Adverb
schoolma'am	Yes	No	No	No
adult female	Yes	No	No	No

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

Other hypernyms of schoolma'am include school teacher, schoolteacher, woman.

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