Full coverage (collision plus comprehensive) extends to a rental vehicle under your existing policy. Liability-only coverage doesn't pay for physical damage to the rental vehicle under any circumstances. Both collision and comprehensive transfer independently, so a policy with only one of the two will have a coverage gap on the corresponding damage type.
Your deductible applies to a rental car claim the same way it applies to your own vehicle; the coverages transfer, but the minimum amount you pay out of pocket doesn't change. Rental reimbursement coverage pays for a replacement car while your own damaged vehicle is being repaired; it's a separate coverage you add to your policy, and it doesn't cover a rental you damaged.










