Yes. What remedy you ask for depends on the type of claim you have, the harm you have suffered or may suffer, the nature of the defendant’s conduct, and the authority of the court itself.
Most civil cases involve a claim for money damages to be paid by one party to the other. Money damages are typically sought to make a person who is injured "whole", or to give a party to a contract the "benefit of the bargain". Money damages may consist of compensatory damages, punitive damages, nominal damages, interest, and attorney’s fees.
The remedy you MIGHT receive frequently depends on the relative strengths of your case and your opponent’s case, your resourcefulness and ability to get all the facts, the ability of both sides’ attorneys to spend the time and effort necessary to do the job that is required.