Clarkie
I can't see where the distinction lies. In both cases you have a passive inertial element (the platter), an active source of energy (the motor, which also has inertia of its own) and a transmission (belt or idler) which links them.
The motor's function is to replace the energy lost from the system. The transmission's function is to adapt the speed of the motor to that of the platter.
Most of the distinctions made betwen belt and idler can be viewed in terms of how lossy the transmission is, it historically having been the case that belt TTs were made with a much lossier form than were idlers.
I think the inertia of the motor is also important but misunderstood.
Mark Kelly