billy club vs nightstick

billy club and nightstick both are nouns.

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

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

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

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

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