supermarket vs food market

supermarket and food market both are nouns.

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

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

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

Other hypernyms of supermarket include grocery, grocery store, market.

supermarket (noun)	food market (noun)
a large self-service grocery store selling groceries and dairy products and household goods	a marketplace where groceries are sold