war crime vs criminal offence

war crime and criminal offence both are nouns.

Word	Noun	Adjective	Verb	Adverb
war crime	Yes	No	No	No
criminal offence	Yes	No	No	No

As nouns, criminal offence is a hypernym of war crime; that is, criminal offence is a word with a broader meaning than war crime:

war crime: a crime committed in wartime; violation of rules of war
criminal offence: (criminal law) an act punishable by law; usually considered an evil act

Other hypernyms of war crime include crime, criminal offense, law-breaking.

war crime (noun)	criminal offence (noun)
a crime committed in wartime; violation of rules of war	(criminal law) an act punishable by law; usually considered an evil act