Comprehensive insurance and third party liability?

I have have to ask, in what context?

Third party liability is where a other party is found liable for some event. (sorry you did not say if industrial, auto, product liability or what type, the exact insurance issue can differ.

The comprehensive liability covers areas where you are specifically at fault and was a party to the event. Again, in what context, auto, business, product or so on.

Also where, Insurance laws are state based in America, (although most use same vocabulary, means can differ slightly. If outside America, where is this, since insurance laws can vary, "greatly"

They are not related at all. Comprehensive can mean broad coverage or Comprehensive in Auto coverage-something hit you, a tree or a deer, hail etc. Third party refers to a structured way of insurance coverage. With typical liability, you are the first party, the person you injure, or damage their property through negligence is the second party and your insurance company is the third party. There must always be 3 parties involved. There are no third party liabilities if you lose control of your car, run off the road and hit a tree. You need collision insurance UNLESS you can show another party caused you to run off the road. In that case, their insurer would be the third party.