exterminator vs slayer

exterminator and slayer both are nouns.

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

As nouns, slayer is a hypernym of exterminator; that is, slayer is a word with a broader meaning than exterminator:

exterminator: someone who exterminates (especially someone whose occupation is the extermination of troublesome rodents and insects)
slayer: someone who causes the death of a person or animal

Other hypernyms of exterminator include killer.

exterminator (noun)	slayer (noun)
someone who exterminates (especially someone whose occupation is the extermination of troublesome rodents and insects)	someone who causes the death of a person or animal