Legal Question in Personal Injury in Maryland

Your question is extremely vague, but I'll try to answer it. A "claim number" generally refers to the number the liability insurance company assigns to it once a claim is reported. A "case number" usually refers to a case filed in court, and is the number assigned by the court which first appears on the complaint and summons. If you are engaging in ADR before filing suit, the company conducting the ADR might utilize its own numbering system, but that number would be different from a court case number.