granny vs old woman

granny and old woman both are nouns.

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

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

granny (noun)	old woman (noun)
a reef knot crossed the wrong way and therefore insecure	a woman who is old
the mother of your father or mother	herb with greyish leaves found along the east coast of North America; used as an ornamental plant
an old woman