old woman vs adult female

old woman and adult female both are nouns.

Word	Noun	Adjective	Verb	Adverb
old woman	Yes	No	No	No
adult female	Yes	No	No	No

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

Other hypernyms of old woman include golden ager, old person, oldster, senior citizen, woman.

old woman (noun)	adult female (noun)
a woman who is old	an adult female person (as opposed to a man)
herb with greyish leaves found along the east coast of North America; used as an ornamental plant