open-air market vs market square

open-air market and market square both are nouns.

Word	Noun	Adjective	Verb	Adverb
open-air market	Yes	No	No	No
market square	Yes	No	No	No

As nouns, open-air market and market square are synonyms defined as:

open-air market and market square: a public marketplace where food and merchandise is sold

Other synonyms of open-air market include open-air marketplace.

open-air market (noun)	market square (noun)
a public marketplace where food and merchandise is sold	a public marketplace where food and merchandise is sold