handkerchief vs piece of cloth

handkerchief and piece of cloth both are nouns.

Word	Noun	Adjective	Verb	Adverb
handkerchief	Yes	No	No	No
piece of cloth	Yes	No	No	No

As nouns, piece of cloth is a hypernym of handkerchief; that is, piece of cloth is a word with a broader meaning than handkerchief:

handkerchief: a square piece of cloth used for wiping the eyes or nose or as a costume accessory
piece of cloth: a separate part consisting of fabric

Other hypernyms of handkerchief include piece of material.

handkerchief (noun)	piece of cloth (noun)
a square piece of cloth used for wiping the eyes or nose or as a costume accessory	a separate part consisting of fabric