capital offense vs law-breaking

capital offense and law-breaking both are nouns.

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

As nouns, law-breaking is a hypernym of capital offense; that is, law-breaking is a word with a broader meaning than capital offense:

capital offense: a crime so serious that capital punishment is considered appropriate
law-breaking: (criminal law) an act punishable by law; usually considered an evil act

Other hypernyms of capital offense include crime, criminal offence, criminal offense.

capital offense (noun)	law-breaking (noun)
a crime so serious that capital punishment is considered appropriate	(criminal law) an act punishable by law; usually considered an evil act