billystick vs billy club

billystick and billy club both are nouns.

Word	Noun	Adjective	Verb	Adverb
billystick	Yes	No	No	No
billy club	Yes	No	No	No

As nouns, billystick and billy club are synonyms defined as:

billystick and billy club: a short stout club used primarily by policemen

Other synonyms of billystick include baton, billy, nightstick, truncheon.

billystick (noun)	billy club (noun)
a short stout club used primarily by policemen	a short stout club used primarily by policemen