gunslinger vs murderer

gunslinger and murderer both are nouns.

Word	Noun	Adjective	Verb	Adverb
gunslinger	Yes	No	No	No
murderer	Yes	No	No	No

As nouns, murderer is a hypernym of gunslinger; that is, murderer is a word with a broader meaning than gunslinger:

gunslinger: a professional killer who uses a gun
murderer: a criminal who commits homicide (who performs the unlawful premeditated killing of another human being)

Other hypernyms of gunslinger include liquidator, manslayer.

gunslinger (noun)	murderer (noun)
a professional killer who uses a gun	a criminal who commits homicide (who performs the unlawful premeditated killing of another human being)