For AC induction motors, current is not closely related to torque. This is because the induction motor needs current to achieve motor flux even if the motor is producing no torque. Above 80% current, the torque and current converge. In web handling not many drives run above 80% current.
In DC motors, provided the shunt field current is held constant, armature current closely follows motor torque. The % torque and % current may be within 2%.
There is only one current limit in an AC variable speed drive (VSD). The purpose of current limit is to do one thing only. That is to protect the motor, not the valuable equipment connected to it. To protect the equipment, you need to use the torque limits.
During commissioning, it is useful to check the current limit (by E-Stop) to ensure that the drive and motor are capable of achieving this current without fault. We learn the most about our equipment when we push it to the limit. The current limit is an electronic function and if the drive has not been set up or tuned correctly, may not operate as expected.