grocery store vs food market

grocery store and food market both are nouns.

Word	Noun	Adjective	Verb	Adverb
grocery store	Yes	No	No	No
food market	Yes	No	No	No

As nouns, grocery store and food market are synonyms defined as:

Other synonyms of grocery store include grocery, market.

grocery store (noun)	food market (noun)
a marketplace where groceries are sold	a marketplace where groceries are sold