murderer vs outlaw

murderer and outlaw both are nouns.

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

As nouns, outlaw is a hypernym of murderer; that is, outlaw 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)
outlaw: someone who has committed a crime or has been legally convicted of a crime

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

murderer (noun)	outlaw (noun)
a criminal who commits homicide (who performs the unlawful premeditated killing of another human being)	someone who has committed a crime or has been legally convicted of a crime

murderer (adjective)	outlaw (adjective)
	contrary to or forbidden by law
	disobedient to or defiant of law

murderer (verb)	outlaw (verb)
	declare illegal; outlaw