Making a claim with “the other driver’s” insurance company? That’s a third-party claim. Driving a company car and sustain an injury? You’re making a third-party claim there, too. Injured while driving your own car in the course of your job? A third-party claim with your employer’s insurance company would be your mechanism for recovery of medical and repair costs. Any claim made to an insurance company other than your own is considered a third-party claim.
When you purchase comprehensive coverage, you will select a set deductible, which is the amount you pay out of pocket toward a covered claim. Let's say you choose a $500 deductible, and your car is later damaged by hail in a covered claim. If it costs $1,500 to repair your car, you would pay your $500 deductible, and your insurance would pay the remaining $1,000.