Collision covers the losses you suffer when your automobile is involved in an accident. For example, if you hit a car parked along the street, the damages to your car will be paid for under your collision coverage.
Comprehensive covers losses to your vehicle not caused by an accident. An example might be a windstorm blowing a tree down on your car. This would be covered under your comprehensive coverage. Your vehicle being stolen would be another example where comprehensive would be applied.
California does not allow No Fault Coverage but, if you have no-fault insurance the people hurt in an accident are paid by their own insurance company regardless of who caused the accident. This is quite different than what happens in the traditional system in California. This system is called the tort system.
Only a dozen or so states have No Fault and in those states you can still sue for pain and suffering if the losses exceed a certain amount.
Insurance requirements vary from state to state. Your current policy may not satisfy those requirements. Your current insurance company may not be licensed to provide insurance in the state you are moving to. When you move you should notify your insurance company immediately and they will let you know if they will be able to continue your policy in that state.
If they do not provide insurance for that state you must start a new policy for the state as soon as possible.