gunman vs murderer

gunman and murderer both are nouns.

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

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

gunman: 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 gunman include liquidator, manslayer.

gunman (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)
a person who shoots a gun (as regards their ability)