What is the difference between positive (active) brakes and the negative brakes?
Positive brakes are actuated by an external force. Negative brakes are actuated by the force of a spring and are released by an external force.
Example: Automobile brakes are positive brakes, actuated by applying foot pressure to a hydraulic piston which presses the brakes. Springs release the brake force.
Negative brakes work in reverse like elevator safety brakes are always closed and the braking force is applied by a spring. Hydraulic or electromagnetic pistons are used to to release the spring force thus releasing the brake.