gunman vs shooter

gunman and shooter both are nouns.

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

As nouns, gunman and shooter are synonyms defined as:

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

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

gunman: 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 gunman include shot.

gunman (noun)	shooter (noun)
a professional killer who uses a gun	a large marble used for shooting in the game of marbles
a person who shoots a gun (as regards their ability)	a person who shoots (usually with respect to their ability to shoot)
	a professional killer who uses a gun
	(sports) a player who drives or kicks a ball at the goal (or a basketball player who shoots at the basket)
	a gambler who throws dice in the game of craps