nightstick vs billy club

nightstick and billy club both are nouns.

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

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

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

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

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