In general the two types of insurance are both voluntary and supplementary to the legally required liability motor vehicle insurance. They only differ in the scope of the insurance benefits.
Partial coverage (Teilkasko)
With partial coverage you insure damages to your own vehicle and is a voluntary insurance, which you can take out in addition to motor vehicle liability insurance. The partial cover insures you in case of fire, explosion, theft, glass breakage or short circuit as well as storm, hail, lightning or flooding. Collisions with game (e.g. a deer) are also covered.
Fully comprehensive coverage (Vollkasko)
Fully comprehensive insurance offers you the most extensive protection. In addition to the partial cover, it covers self-inflicted damage to your car, malicious damage caused by vandalism and damage after hit and run.
Please note that this insurance cover can be important for new and expensive, as well as for leasing vehicles.