The term "full coverage" is used by most people when referring to Physical Damage coverage. That means they have Liability insurance and Physical Damage, sometimes along with other coverage combinations to be fully covered.
Physical damage coverage consists of collision and comprehensive coverage. Generally, collision insurance covers damage to ONLY your automobile caused by collision with another object or by upset. Comprehensive insurance covers damage to ONLY your automobile from vandalism, theft, glass breakage, or anything Other Than Collision.
Most loss payees, lien holders, and leasing companies require Physical Damage coverage if you are financing or leasing your vehicle.
These coverages do not extend to other vehicles and they will not cover your friend's vehicle or become secondary insurance behind another vehicles primary insurance. Your friend's liability coverage would be "primary," and you liability coverage will be "excess or secondary" to the liability coverages.
Comment Update: No, the coverage will not extend. Sorry.