bandana vs handkerchief

bandana and handkerchief both are nouns.

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

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

bandana: 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 bandana include hankey, hankie, hanky.

bandana (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