pocket-handkerchief vs hanky

pocket-handkerchief and hanky both are nouns.

Word	Noun	Adjective	Verb	Adverb
pocket-handkerchief	Yes	No	No	No
hanky	Yes	No	No	No

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

pocket-handkerchief: a handkerchief that is carried in a pocket
hanky: a square piece of cloth used for wiping the eyes or nose or as a costume accessory

Other hypernyms of pocket-handkerchief include handkerchief, hankey, hankie.

pocket-handkerchief (noun)	hanky (noun)
a handkerchief that is carried in a pocket	a square piece of cloth used for wiping the eyes or nose or as a costume accessory