gun vs shooter

gun and shooter both are nouns.

Word	Noun	Adjective	Verb	Adverb
gun	Yes	No	Yes	No
shooter	Yes	No	No	No

As nouns, gun and shooter are synonyms defined as:

Other synonyms of gun include gun for hire, gunman, gunslinger, hired gun, hit man, hitman, torpedo, triggerman.

As nouns, shooter is a hypernym of gun; that is, shooter is a word with a broader meaning than gun:

gun: a person who shoots a gun (as regards their ability)
shooter: a person who shoots (usually with respect to their ability to shoot)

Other hypernyms of gun include shot.

gun (noun)	shooter (noun)
the discharge of a firearm as signal or as a salute in military ceremonies	a large marble used for shooting in the game of marbles
a weapon that discharges a missile at high velocity (especially from a metal tube or barrel)	a person who shoots (usually with respect to their ability to shoot)
large but transportable armament	a professional killer who uses a gun
a hand-operated pump that resembles a pistol; forces grease into parts of a machine	(sports) a player who drives or kicks a ball at the goal (or a basketball player who shoots at the basket)
a pedal that controls the throttle valve	a gambler who throws dice in the game of craps
a professional killer who uses a gun
a person who shoots a gun (as regards their ability)

gun (verb)	shooter (verb)
shoot with a gun