war crime vs criminal offense

war crime and criminal offense both are nouns.

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

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

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

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

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