grocery store vs market

grocery store and market both are nouns.

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

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

Other synonyms of grocery store include food market, grocery.

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

Other hypernyms of grocery store include market place, marketplace, mart.

grocery store (noun)	market (noun)
a marketplace where groceries are sold	the world of commercial activity where goods and services are bought and sold
	a marketplace where groceries are sold
	an area in a town where a public mercantile establishment is set up
	the customers for a particular product or service
	the securities markets in the aggregate

grocery store (verb)	market (verb)
	make commercial
	engage in the commercial promotion, sale, or distribution of
	deal in a market
	buy household supplies