serial murderer vs serial killer

serial murderer and serial killer both are nouns.

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

As nouns, serial murderer and serial killer are synonyms defined as:

serial murderer and serial killer: someone who murders more than three victims one at a time in a relatively short interval

serial murderer (noun)	serial killer (noun)
someone who murders more than three victims one at a time in a relatively short interval	someone who murders more than three victims one at a time in a relatively short interval