piece of paper vs leaf

piece of paper and leaf both are nouns.

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

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

piece of paper: paper used for writing or printing
leaf: 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, folio, tear sheet, foolscap, style sheet, worksheet, revenue stamp, stamp.

piece of paper (noun)	leaf (noun)
paper used for writing or printing	hinged or detachable flat section (as of a table or door)
	a sheet of any written or printed material (especially in a manuscript or book)
	the main organ of photosynthesis and transpiration in higher plants

piece of paper (verb)	leaf (verb)
	produce leaves, of plants
	turn over pages
	look through a book or other written material