old woman vs witch

old woman and witch both are nouns.

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

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

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

old woman (noun)	witch (noun)
a woman who is old	a female sorcerer or magician
herb with greyish leaves found along the east coast of North America; used as an ornamental plant	a being (usually female) imagined to have special powers derived from the devil
	an ugly evil-looking old woman
	a believer in Wicca

old woman (verb)	witch (verb)
	cast a spell over someone or something; put a hex on someone or something