1. 

   Static Torque

   There is no (or very little) rotation. No moving parts! A common example is measurement of tightening torque. These applications call for a Reaction Torquemeter. It may be flanged (as in the photo above), or an instrumented shaft.
2. 

   Rotating-shaft Torque

   In this application, the shaft is free to rotate, even at thousands of rpm! A common example is when a motor drives a fan or pump. If knowing rotation SPEED is also of interest, we add a speed pickup to the Torquemeter. Then shaft POWER can be readily computed!