piece vs cutting

piece and cutting both are nouns.

Word	Noun	Adjective	Verb	Adverb
piece	Yes	No	Yes	No
cutting	Yes	Yes	No	No

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

Other hyponyms of piece include body part, corpus, acicula, base, corner, craton, fragment, hunk, lump, nub, stub, segment, slice, strip, world.

piece (noun)	cutting (noun)
a separate part of a whole	the act of shortening something by chopping off the ends
game equipment consisting of an object used in playing certain board games	the act of cutting something into parts
a portable gun	the act of penetrating or opening open with a sharp edge
a work of art of some artistic value	the activity of selecting the scenes to be shown and putting them together to create a film
an item that is an instance of some type	the act of diluting something
a distance	removing parts from hard material to create a desired pattern or shape
a musical work that has been created	the division of a deck of cards before dealing
an artistic or literary composition	an excerpt cut from a newspaper or magazine
an instance of some kind	a piece cut off from the main part of something
a serving that has been cut from a larger portion	a part (sometimes a root or leaf or bud) removed from a plant to propagate a new plant through rooting or grafting
a portion of a natural object
a share of something
a period of indeterminate length (usually short) marked by some action or condition

piece (adjective)	cutting (adjective)
	unpleasantly cold and damp
	painful as if caused by a sharp instrument
	(of speech) harsh or hurtful in tone or character

piece (verb)	cutting (verb)
repair by adding pieces
eat intermittently; take small bites of
join during spinning
to join or unite the pieces of
create by putting components or members together