Generally, Collision insurance covers damage to your automobile caused by collision with another object or by upset. Comprehensive insurance covers damage to your automobile for things other than Collision so for vandalism, hitting an animal, hail damage, flood water, theft or glass breakage.
If you are making payments on your vehicle, your lien holder will usually require you carry these physical damage coverages. They require these coverages, because they cover the vehicle up to its actual cash value and until the car is paid off the vehicle technically belongs to them. However, if your vehicle is paid for, it is your choice to purchase Comprehensive and Collision coverages.
Now, some insurance companies will not sell Comprehensive coverage without the Collision coverage. And, some insurance companies will require you keep the deductible amount the same for both coverages. In order to determine if these coverages are worth purchasing, you will need to weigh the value of your vehicle against your deductible amount and the premium you will be paying for the coverages. An older vehicle that does not have much value isn't typically insured for Comprehensive and Collision coverage. If however you have a newer car and you want to protect your asset by having coverage you can place a claim against for covered accidents than you would normally want both Collision and Comprehensive on your vehicle.
Come here to get a quote for California state automobile insurance (or for automobile insurance for any other state in the United States) to compare your rates with and without full coverage of Collision and Comprehensive.