vice crime vs criminal offense

vice crime and criminal offense both are nouns.

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

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

vice crime: a vice that is illegal
criminal offense: (criminal law) an act punishable by law; usually considered an evil act

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

vice crime (noun)	criminal offense (noun)
a vice that is illegal	(criminal law) an act punishable by law; usually considered an evil act