1. Comprehensive cover as it's name implies, is the most complete and common type. It is required by most financing companies.
2. Less common ones are A) Third Party, Fire, and Theft covers fire, vandalism, theft to your vehicle. Additionally it covers damages to the other party and B) Third Party Only is the cheapest of all. In the event of claim and it is your fault, it will only pay out to the other party but not your own repair.