hired gun vs murderer

hired gun and murderer both are nouns.

Word	Noun	Adjective	Verb	Adverb
hired gun	Yes	No	No	No
murderer	Yes	No	No	No

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

hired gun: 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 hired gun include liquidator, manslayer.

hired gun (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)