toupee vs false hair

toupee and false hair both are nouns.

Word	Noun	Adjective	Verb	Adverb
toupee	Yes	No	No	No
false hair	Yes	No	No	No

As nouns, false hair is a hypernym of toupee; that is, false hair is a word with a broader meaning than toupee:

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

Other hypernyms of toupee include hairpiece, postiche.

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