If you have full coverage ( comp and collision) on a vehicle you own, you have the same coverage on a vehicle you rent. So in the event of damage to a rented vehicle it would be covered the same as if you owned it. However, there are potentially other charges the rental company may apply that your personal auto policy will not cover.
Diminished value of the damaged vehicle could be charged to you. For example, if the vehicle was worth $30,000 before you damaged it, and after the damage was repaired the vehicle now has a value of $25,000, you could be charged the $5,000 difference in value. You could also be charged for loss of use. This is the time that the damaged vehicle is out of service waiting to be repaired. You could be charged the daily rental fee for every day the vehicle is out of service.
Before you rent a vehicle always check with your insurance agent. In most cases your policy can be endorsed to cover these additional costs' for a small increase in premium. You can also purchase these coverages at the rental counter.
To be sure, always check with your agent!