public square vs piazza

public square and piazza both are nouns.

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

As nouns, piazza is a hyponym of public square; that is, piazza is a word with a more specific, narrower meaning than public square:

Other hyponyms of public square include place, plaza.

public square (noun)	piazza (noun)
a place of assembly for the people in ancient Greece	a public square with room for pedestrians
an open area at the meeting of two or more streets