slip of paper vs piece of paper

slip of paper and piece of paper both are nouns.

Word	Noun	Adjective	Verb	Adverb
slip of paper	Yes	No	No	No
piece of paper	Yes	No	No	No

As nouns, piece of paper is a hypernym of slip of paper; that is, piece of paper is a word with a broader meaning than slip of paper:

Other hypernyms of slip of paper include sheet, sheet of paper.

slip of paper (noun)	piece of paper (noun)
a small sheet of paper	paper used for writing or printing