serial killer vs murderer

serial killer and murderer both are nouns.

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

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

serial killer: someone who murders more than three victims one at a time in a relatively short interval
murderer: a criminal who commits homicide (who performs the unlawful premeditated killing of another human being)

Other hypernyms of serial killer include liquidator, manslayer.

serial killer (noun)	murderer (noun)
someone who murders more than three victims one at a time in a relatively short interval	a criminal who commits homicide (who performs the unlawful premeditated killing of another human being)