Nick,
Turboprops are characterized by high mass flow through the props, low velocity increase. For a prop aircraft maximum thrust (of the engine prop combination aka power plant) is at zero speed.
The power plant power output (prop + engine) increases with airspeed to a point then decreases.
The turboprop engine is a power producing device, with most of the work done by the gas stream converted in shaft horse power for transmission to gearbox then to the prop.
The turboprop power plant gets most of its thrust from accelerating air through props, only about 10-25% total thrust from the power plant comes from the jet exhaust.
As most of the useful energy output from the engine is in the form of shaft horse power (ie torque and RPM) it makes sense to classify its ability in terms of shaft output, as only a small fraction (10-25%) is gas stream output
As thrust drops off with speed its not a very useful operational parameter. i.e imagine trying to set a thrust figure while the aircraft is moving on a takeoff roll, its decreasing as the speed builds up, much easier to set a torque and temperature to get the power required.
Jets, characterized by low mass flow of the air stream with a high velocity increase. The thrust available through a range of speeds is fairly constant for a jet. To get the performance you want set the thrust via fuel flow, shaft RPM, or engine pressure ratio. This sets the thrust, as airspeed increase, thrust remains fairly constant, and power increases.
The turbojet derives most of the engine performance from the high velocity exhaust gas in the form of jet thrust, with only a small percentage of the gas stream energy used to drive the compressor.
The jet exhaust is doing most of what is useful, hence the jet thrust is used figure people look at, plus its operationally easy to determine.
Now for something to really confuse you, a turbofan derives most of its performance from the larger bypass fans at low altitudes (the high mass flow bit on the fan), and the jet thrust (the high exhaust gas stream velocity) at high altitudes.
Z