public executioner vs killer

public executioner and killer both are nouns.

Word	Noun	Adjective	Verb	Adverb
public executioner	Yes	No	No	No
killer	Yes	No	No	No

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

public executioner: an official who inflicts capital punishment in pursuit of a warrant
killer: someone who causes the death of a person or animal

Other hypernyms of public executioner include slayer.

public executioner (noun)	killer (noun)
an official who inflicts capital punishment in pursuit of a warrant	predatory black-and-white toothed whale with large dorsal fin; common in cold seas
	a difficulty that is hard to deal with
	someone who causes the death of a person or animal
	the causal agent resulting in death