supermarket vs grocery store

supermarket and grocery store both are nouns.

Word	Noun	Adjective	Verb	Adverb
supermarket	Yes	No	No	No
grocery store	Yes	No	No	No

As nouns, grocery store is a hypernym of supermarket; that is, grocery store is a word with a broader meaning than supermarket:

supermarket: a large self-service grocery store selling groceries and dairy products and household goods
grocery store: a marketplace where groceries are sold

Other hypernyms of supermarket include food market, grocery, market.

supermarket (noun)	grocery store (noun)
a large self-service grocery store selling groceries and dairy products and household goods	a marketplace where groceries are sold