hairpiece vs wig

hairpiece and wig both are nouns.

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

As nouns, wig is a hyponym of hairpiece; that is, wig 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
wig: hairpiece covering the head and made of real or synthetic hair

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

hairpiece (noun)	wig (noun)
a covering or bunch of human or artificial hair used for disguise or adornment	hairpiece covering the head and made of real or synthetic hair
	British slang for a scolding