Had crime vs criminal offence

Had crime and criminal offence both are nouns.

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

As nouns, criminal offence is a hypernym of Had crime; that is, criminal offence 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 offence: (criminal law) an act punishable by law; usually considered an evil act

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

Had crime (noun)	criminal offence (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