Hit and run criminal charges focus on the offender paying their debt to society. They may be put in jail and ordered to pay a fine. A civil claim is about the legal responsibility of the offender to the victim and the harm that the victim endures.
There are differences between the two types of proceedings, including a lower burden of proof in a civil claim, the possibility of non-economic damages, and the right of the victim to control decisions during the litigation rather than a prosecutor.