offense vs law-breaking

offense and law-breaking both are nouns.

Word	Noun	Adjective	Verb	Adverb
offense	Yes	No	No	No
law-breaking	Yes	No	No	No

As nouns, law-breaking is a hyponym of offense; that is, law-breaking is a word with a more specific, narrower meaning than offense:

offense: a transgression that constitutes a violation of what is judged to be right
law-breaking: (criminal law) an act punishable by law; usually considered an evil act

Other hyponyms of offense include crime, criminal offence, criminal offense.

offense (noun)	law-breaking (noun)
the action of attacking an enemy	(criminal law) an act punishable by law; usually considered an evil act
a transgression that constitutes a violation of what is judged to be right
a lack of politeness; a failure to show regard for others; wounding the feelings of others
a feeling of anger caused by being offended
the team that has the ball (or puck) and is trying to score