DOES auto insurance COVER you or your auto?

It depends upon the kind of insurance to which you are referring.

Physical damage coverage (collision and comprehensive) covers physical damage to the vehicle insured according to the policy terms.

Liability insurance protects you from claims by third parties who may have sustained damages as a result of your careless in operating an insured vehicle. The scope of damages can be either property damage or bodily injury damages.

Personal Injury Protection insurance (often referred to as PIP or no-fault coverage) pays a portion of your own medical expenses and lost wages if you are injured in a collision.

The insurance follows the vehicle, not the driver, so if you are a driver in another vehicle, that person's insurance is the primary insurance company unless their limits are too low and then the driver's insurance company would provide excess coverage.