hag vs old woman

hag and old woman both are nouns.

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

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

hag (noun)	old woman (noun)
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	a woman who is old
an ugly evil-looking old woman	herb with greyish leaves found along the east coast of North America; used as an ornamental plant