hatchet man vs murderer

hatchet man and murderer both are nouns.

Word	Noun	Adjective	Verb	Adverb
hatchet man	Yes	No	No	No
murderer	Yes	No	No	No

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

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

Other hypernyms of hatchet man include liquidator, manslayer.

hatchet man (noun)	murderer (noun)
one whose job it is to execute unpleasant tasks for a superior	a criminal who commits homicide (who performs the unlawful premeditated killing of another human being)
a professional killer