first offender vs convict

first offender and convict both are nouns.

Word	Noun	Adjective	Verb	Adverb
first offender	Yes	No	No	No
convict	Yes	No	Yes	No

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

first offender (noun)	convict (noun)
someone convicted for the first time	a person serving a sentence in a jail or prison
	a person who has been convicted of a criminal offense

first offender (verb)	convict (verb)
	find or declare guilty