ex-wife vs woman

ex-wife and woman both are nouns.

Word	Noun	Adjective	Verb	Adverb
ex-wife	Yes	No	No	No
woman	Yes	No	No	No

As nouns, woman is a hypernym of ex-wife; that is, woman is a word with a broader meaning than ex-wife:

Other hypernyms of ex-wife include adult female.

ex-wife (noun)	woman (noun)
a woman who was formerly a particular man's wife	women as a class
	an adult female person (as opposed to a man)
	a female person who plays a significant role (wife or mistress or girlfriend) in the life of a particular man