public square vs market

public square and market both are nouns.

Word	Noun	Adjective	Verb	Adverb
public square	Yes	No	No	No
market	Yes	No	Yes	No

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

Other hypernyms of public square include market place, marketplace, mart.

public square (noun)	market (noun)
a place of assembly for the people in ancient Greece	the world of commercial activity where goods and services are bought and sold
an open area at the meeting of two or more streets	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

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