Someone who commits crimes:

criminal, offender, thief, robber, burglar, shoplifter, attacker, mugger, murderer, rapist

Punishments:

-sentence – a punishment given by a judge in a court
-fine – an amount of money that you must pay as a punishment
-penalty – a general word for a punishment given to someone who has broken a law, rule or agreement
-death sentence/ death penalty/ capital punishment
-community service – unpaid work helping other people that someone does as punishment for a crime
-corporal punishment – when someone punishes a child by hitting them