No, these two types of the coverage are not identical. In all states, you are required to carry Property Damage Liability coverage, which covers damage you cause to someone else's car or property (the property you hit). There is typically no deductible for this coverage.
Physical Damage (referred to as Comprehensive and Collision) is an optional coverage that pays for damage to your car. Collision covers damage from your car colliding with another car or object. Comprehensive covers damage from events such as fire, theft, vandalism, weather, and windshield or animal-related accidents. Comprehensive and Collision usually have separate deductibles and they are usually required if you have a loan on your vehicle.
Any time you see the term Liability, the coverage is paying for someone else's damages that you cause (are liable for).