food market vs grocery

food market and grocery both are nouns.

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

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

Other synonyms of food market include grocery store, market.

food market (noun)	grocery (noun)
a marketplace where groceries are sold	a marketplace where groceries are sold
	(usually plural) consumer goods sold by a grocer