piece of paper vs folio

piece of paper and folio both are nouns.

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

As nouns, folio is a hyponym of piece of paper; that is, folio is a word with a more specific, narrower meaning than piece of paper:

piece of paper: paper used for writing or printing
folio: a sheet of any written or printed material (especially in a manuscript or book)

Other hyponyms of piece of paper include slip, slip of paper, signature, leaf, tear sheet, foolscap, style sheet, worksheet, revenue stamp, stamp.

piece of paper (noun)	folio (noun)
paper used for writing or printing	a book (or manuscript) consisting of large sheets of paper folded in the middle to make two leaves or four pages
	a sheet of any written or printed material (especially in a manuscript or book)
	the system of numbering pages