murderer vs slayer

murderer and slayer both are nouns.

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

As nouns, slayer is a hypernym of murderer; that is, slayer 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)
slayer: someone who causes the death of a person or animal

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

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