wife vs better half

wife and better half both are nouns.

Word	Noun	Adjective	Verb	Adverb
wife	Yes	No	No	No
better half	Yes	No	No	No

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

Other hypernyms of wife include married person, mate, partner, spouse, adult female, woman.

wife (noun)	better half (noun)
a married woman; a man's partner in marriage	a person's partner in marriage