How does torque differ from force?
Force is a vector (applied in a straight line, with the acceleration in the same direction as the net force).
You push your car with a force, but you apply torque to the lug nut to loosen it in order to change your tire. With torque, you talk about force at a distance, and angular acceleration instead of linear acceleration.
Force has units of Newtons, while torque, being the product of a force and a distance, has units of Newton
Torque and force also differ in that force is a true vector, whereas torque is a pseudovector, that is, it picks up a sign flip under certain kinds of coordinate transformations.
In terms of derivatives, force is the time derivative of the linear momentum:
while torque is the time derivative of angular momentum: