felony vs criminal offense

felony and criminal offense both are nouns.

Word	Noun	Adjective	Verb	Adverb
felony	Yes	No	No	No
criminal offense	Yes	No	No	No

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

felony: a serious crime (such as murder or arson)
criminal offense: (criminal law) an act punishable by law; usually considered an evil act

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

felony (noun)	criminal offense (noun)
a serious crime (such as murder or arson)	(criminal law) an act punishable by law; usually considered an evil act