hairpiece vs toupee

hairpiece and toupee both are nouns.

Word	Noun	Adjective	Verb	Adverb
hairpiece	Yes	No	No	No
toupee	Yes	No	No	No

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

hairpiece: a covering or bunch of human or artificial hair used for disguise or adornment
toupee: a small hairpiece to cover partial baldness

Other hyponyms of hairpiece include Afro-wig, switch, toupe, wig.

hairpiece (noun)	toupee (noun)
a covering or bunch of human or artificial hair used for disguise or adornment	a small hairpiece to cover partial baldness