pizza shop vs pizza parlor

pizza shop and pizza parlor both are nouns.

Word	Noun	Adjective	Verb	Adverb
pizza shop	Yes	No	No	No
pizza parlor	Yes	No	No	No

As nouns, pizza shop and pizza parlor are synonyms defined as:

Other synonyms of pizza shop include pizzeria.

pizza shop (noun)	pizza parlor (noun)
a shop where pizzas are made and sold	a shop where pizzas are made and sold