wife vs adult female

wife and adult female both are nouns.

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

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

Other hypernyms of wife include better half, married person, mate, partner, spouse, woman.

wife (noun)	adult female (noun)
a married woman; a man's partner in marriage	an adult female person (as opposed to a man)