murderer vs killer

murderer and killer both are nouns.

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

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

murderer: a criminal who commits homicide (who performs the unlawful premeditated killing of another human being)
killer: someone who causes the death of a person or animal

Other hypernyms of murderer include criminal, crook, felon, malefactor, outlaw, slayer.

murderer (noun)	killer (noun)
a criminal who commits homicide (who performs the unlawful premeditated killing of another human being)	predatory black-and-white toothed whale with large dorsal fin; common in cold seas
	a difficulty that is hard to deal with
	someone who causes the death of a person or animal
	the causal agent resulting in death