Mach trim is a sub function of auto stab trim. All it does is tries to keep the elevators fared by moving the stab to nullify the input. It will do this if the elevators have been displaced from the fared condition by a constant amount for a pre determined amount of time - fifteen seconds in the case of the 747, ten in the case of the 767 ( I think ). The time delay is intended to prevent the auto stab trim gizmos chasing the autopilot, which could lead to porpoising.
The mechanics and signalling are different between the all of the Boeings, but the concept is fundamentally the same.
BTW, a Boeing SRP ( Service Related Problem ) regarding a stab trim seizure on a 767 has been classified as non safety, as in their opinion the aircraft can still be flown to a safe landing with the stab fully displaced one way or the other.
Wouldn't like to put that to the test myself.