bandanna vs handkerchief

bandanna and handkerchief both are nouns.

Word	Noun	Adjective	Verb	Adverb
bandanna	Yes	No	No	No
handkerchief	Yes	No	No	No

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

bandanna: large and brightly colored handkerchief; often used as a neckerchief
handkerchief: a square piece of cloth used for wiping the eyes or nose or as a costume accessory

Other hypernyms of bandanna include hankey, hankie, hanky.

bandanna (noun)	handkerchief (noun)
large and brightly colored handkerchief; often used as a neckerchief	a square piece of cloth used for wiping the eyes or nose or as a costume accessory