What is a torque motor exactly?
Torque motors are not "exactly" any one thing.

A torque motor can be any type of motor that is designed to operate continuously while stalled or turning very slowly. It can apply torque to a load without actually turning at all. An ordinary motor, even one that normally operates at a low speed, will overheat if stalled for very long. In order to tolerate stalled operation, torque motors must be designed to dissipate more heat than an ordinary motor. They must also be designed to not draw a level of stalled current that is out of proportion to torque.

Brushed DC motors with either wound stators or permanent magnets, brushless DC motors and induction motors have been used for torque motors. When induction motors are used, they are designed with high resistance rotors so that they have high slip and high stalled torque without drawing excessive current. There are currently several competing technologies on the market. There may be other technologies that have been used in the past and technologies that are not widely known because they have very specialized uses. The applications for torque motors are probably mostly more specialized than the applications of ordinary motors.

That is the general idea of what a torque motor is, but there is likely quite a bit more that can be discovered with sufficient research.