headscarf vs kerchief

headscarf and kerchief both are nouns.

Word	Noun	Adjective	Verb	Adverb
headscarf	Yes	No	No	No
kerchief	Yes	No	No	No

As nouns, kerchief is a hypernym of headscarf; that is, kerchief is a word with a broader meaning than headscarf:

headscarf: a kerchief worn over the head and tied under the chin
kerchief: a square scarf that is folded into a triangle and worn over the head or about the neck

headscarf (noun)	kerchief (noun)
a kerchief worn over the head and tied under the chin	a square scarf that is folded into a triangle and worn over the head or about the neck