Comprehensive and collision, both physical damage coverages, pay to repair your vehicle - but in different situations. Comprehensive pays for damage caused by hail, fire, theft, vandalism, and animal hits. Collision covers crash-related vehicle repairs.
Comprehesive, sometimes referred to as 'other than collision,' may or may not have a deductible. Collision always has a deductible. Review your insurance policy declarations page for the specific deducble amount. This is how much you owe out-of-pocket before the insurer begins paying.
A liability-only policy does not cover damage to your vehicle. There is no state program that will take care of your deductible or fix your car if you hit a deer.
Repairs from a deer hit may cost thousands of dollars, but swerving to avoid the animal increases the risk of personal injury. Better to brace yourself, take your foot off the gas pedal, hold tight to the steering wheel, and make contact with the deer.
A comprehensive claim does not lead to an accident surcharge on the policy. However, a claim could result in the loss of a claim-free discount or other action. The renewal premium may increase following a collision claim.