horse-pistol vs side arm

horse-pistol and side arm both are nouns.

Word	Noun	Adjective	Verb	Adverb
horse-pistol	Yes	No	No	No
side arm	Yes	No	No	No

As nouns, side arm is a hypernym of horse-pistol; that is, side arm is a word with a broader meaning than horse-pistol:

horse-pistol: a large pistol (usually in a holster) formerly carried by horsemen
side arm: a firearm that is held and fired with one hand

Other hypernyms of horse-pistol include handgun, pistol, shooting iron.

horse-pistol (noun)	side arm (noun)
a large pistol (usually in a holster) formerly carried by horsemen	a firearm that is held and fired with one hand