Civil suits are intended to serve both purposes - compensation and deterrent (punitive vs compensatory damages). E.g. if you sue a company for doing you damage, the compensatory damages are based only on the injury you suffered, but punitive damages' presence and severity is affected by things like the level of negligence of the company.

The theoretical difference with criminal charges is that criminal charges deal with harms to the difference sovereign (ie the state and the public) that need to be punished regardless of the wishes of the immediate victim. e.g. you're not allowed to settle a murder charge out of court.