spokeswoman vs adult female

spokeswoman and adult female both are nouns.

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

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

Other hypernyms of spokeswoman include interpreter, representative, spokesperson, voice, woman.

spokeswoman (noun)	adult female (noun)
a female spokesperson	an adult female person (as opposed to a man)