Trip Free Circuit Breakers are circuit breakers which can trip even if they are held in the "ON" position. Hence, it is not possible to forcibly keep them in the closed position. Trip free circuit breakers are used in circuits with equipment which are sensitive to overload and in circuits which are not critical.
Non-Trip Free circuit breakers are used in circuits which are critical for plant operation and for safety. In these systems, it may be economical to lose a motor or a heater than to interrupt the manufacturing process. In these circuit breakers, the trip function can be bypassed by forcing the circuit breaker to the on position.