grocery vs supermarket

grocery and supermarket both are nouns.

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

As nouns, supermarket is a hyponym of grocery; that is, supermarket is a word with a more specific, narrower meaning than grocery:

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

Other hyponyms of grocery include greengrocery.

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