Thanks Reverse,
I popped "loss of thrust" into the "loss of control" definition following Nick's lead to simplify the way these things are broken down into so many different names. If you lose thrust (ie tail rotor separation or drive shaft break), then you have lost control of the yaw system, and so that is why it was grouped in with stuck pedals, etc.
So the formal definition of Loss of Tail rotor Thrust: The tail rotor system ceases to produce thrust and therefore there is no longer any counter to torque reaction. This is a true emergency that, if in a hover, results in a rapid yaw against the power pedal, quickly achieving extreme rotation. As the vertical stabiliser achieves some measure of counter to torque reaction increasing with forward speed, the rate of yaw therefore dissipates with forward speed, and some types are able to maintain a semblance of a straight line and level flight at cruise speed even after a loss of tail rotor thrust! The loss of thrust may also be coupled with a significant shift in the CofG if associated with tail rotor system structural separation.
The recovery for loss of tail rotor thrust is entirely dependant upon the speed, hieght, and type of aircraft and is covered in the flight manual. Generally that would be to maintain forward flight at speed until near a suitable landing area, then conduct an engine off autorotative style approach. If you have not been able to maintain forward flight, you must remove torque by retarding the engine/s and conduct an autorotative style approach.
Loss of tail rotor thrust is not related to LTE/LTA in any way, as in both LTE and LTA, the tail rotor continues to produce thrust. Unfortunately, due to the high yaw rates experienced with LTE events, pilots can easily assume a loss of tail rotor thrust event instead.
In fact Bell recommended that pilots suffering an LTE event attempt to lower power to stop the yaw, then if not successful, roll the throttle off similarly to the reaction required following a loss of thrust incident. Following an Australian Army B206 LTE event in which the pilot experienced and LTE event at approx 50ft whilst terminating to a hover and carried out the Bell recommended checklist actions perfectly, a deeper analysis of the checklist requirements were undertaken and subsequently revised - at least in the Australian Army. Over adverse terrain, they now recommend accepting the yaw rate, using collective to ensure adequate ground separation (even if that means pulling power!) until sufficient height exists to lower the collective and fly away.
The trick then is to recognise an LTE event from LTA from a Loss of thrust event. Pulling more power in an LTA or loss of thrust event will be very unpleasant!
That is why so many people bang on about not calling these sorts of accidents LTE when they most clearly are not. Hope that helps.