counterwoman vs adult female

counterwoman and adult female both are nouns.

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

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

Other hypernyms of counterwoman include counterperson, woman.

counterwoman (noun)	adult female (noun)
a female who attends a counter (as in a diner)	an adult female person (as opposed to a man)