stateswoman vs adult female

stateswoman and adult female both are nouns.

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

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

Other hypernyms of stateswoman include national leader, solon, woman.

stateswoman (noun)	adult female (noun)
a woman statesman	an adult female person (as opposed to a man)