killer vs murderer

killer and murderer both are nouns.

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

As nouns, murderer is a hyponym of killer; that is, murderer is a word with a more specific, narrower meaning than killer:

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

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