Third Party Insurance is a Liability insurance purchased by the insured (first party) from an insurance company (second party) for protection against possible suits brought by another (third party).

The basic insurance/third-party liability covers third-party persons. But if you have comprehensive car insurance, it not only covers you, third-party persons but also your car.

Third party liability insurance is useful if you are blamed for having caused an accident and someone wishes to file a claim against you. With third party insurance you are insured for claims up to a predetermined amount.

The third party is the injured party to whom any compensation is paid

Yes, Blue Cross Blue Shield Insurance company is a third party payer just as all medical insurance companies are third party payers.