Subrogation
Subrogation is the right an insurer gains, after paying a claim, to step into your position and recover that payment from whoever caused the loss.
If your own insurer pays for repairs to your vehicle, it can then pursue the at-fault driver’s insurer to recover what it paid out, using your legal right to do so. This usually happens behind the scenes and does not require you to take any action once your own damage claim is settled.
Subrogation applies to vehicle damage claims between insurers. It does not affect your separate right to claim compensation for your own injuries from the at-fault driver’s insurer.
How an own damage claim runs explains where subrogation fits into that process.