Had crime vs criminal offense

Had crime and criminal offense both are nouns.

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

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

Had crime: (Islam) serious crimes committed by Muslims and punishable by punishments established in the Koran
criminal offense: (criminal law) an act punishable by law; usually considered an evil act

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

Had crime (noun)	criminal offense (noun)
(Islam) serious crimes committed by Muslims and punishable by punishments established in the Koran	(criminal law) an act punishable by law; usually considered an evil act