cheater vs offender

cheater and offender both are nouns.

Word	Noun	Adjective	Verb	Adverb
cheater	Yes	No	No	No
offender	Yes	No	No	No

As nouns, offender is a hypernym of cheater; that is, offender is a word with a broader meaning than cheater:

Other hypernyms of cheater include wrongdoer.

cheater (noun)	offender (noun)
someone who leads you to believe something that is not true	a person who transgresses moral or civil law