old woman vs hag

old woman and hag both are nouns.

Word	Noun	Adjective	Verb	Adverb
old woman	Yes	No	No	No
hag	Yes	No	No	No

As nouns, hag is a hyponym of old woman; that is, hag is a word with a more specific, narrower meaning than old woman:

Other hyponyms of old woman include beldam, beldame, granny, beldam, beldame, crone, witch, mother.

old woman (noun)	hag (noun)
a woman who is old	eellike cyclostome having a tongue with horny teeth in a round mouth surrounded by eight tentacles; feeds on dead or trapped fishes by boring into their bodies
herb with greyish leaves found along the east coast of North America; used as an ornamental plant	an ugly evil-looking old woman