What is the difference between justice by retribution and justice by restitution?
Retributive justice is the idea that justice can be achieved through punishment for a crime. So if a person commits murder, they are sent to prison for life or executed. Through the punishment of the individual (which also acts, theoretically, as a deterrent to other would-be criminals) society exacts justice. Modern concepts of retributive justice emphasize that punishments ought to be proportional to the crime. So retributive justice is not achieved by executing someone for theft.
Justice by restitution, or "restorative justice," requires the perpetrator of a crime to make amends for their crime, usually by paying financial damages. Restitution may also include paying medical bills or paying for repairs to property, including automobiles. The idea is that achieving retributive justice is perhaps not enough, that the knowledge that a criminal has been punished for their actions does not provide justice for someone who suffered financial loss as a result of their victimhood.
To answer this question, we need to look at the definition of the words retribution and restitution.
The word retribution has a vengeful connotation to it and it refers to somebody being punished for a crime that they have committed. For example a murderer will be sent to prison in retribution for his actions.
Restorative justice, on the other hand, refers to giving back something that was lost because of your actions. If you steal money, for example, you could be required to pay the money back. Perhaps a more common example would be paying someone's medical bills if you accidentally ran them over with your car. Restorative justice could also involve compensating them for their loss of income while they are recuperating.