food market vs grocery store

food market and grocery store both are nouns.

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

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

Other synonyms of food market include grocery, market.

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