What many people term as 'full coverage' is in all reality collision coverage and comprehensive coverage or together they are called physical damage coverage. If you do indeed have these coverages, along with the liability, both your car and the parked car that you hit should be covered.

A comprehensive policy will cover damage to your car when your car hits, or is hit by, another vehicle or object. You will need to pay your deductible to get your car repaired though.