truncheon vs billy club

truncheon and billy club both are nouns.

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

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

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

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

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