Continuous rated torque is the motor's continuous torque that it can output at rated speed, close to the max speed of the motor. This is a better judge of the motor's performance as it's the motor's torque at speed.
Continuous stall torque is the motor's continuous torque at 0 speed (at stall). This is the locked rotor torque. Manufacturers test this by locking the rotor and then monitoring the motor temperature as current is powered into the motor.
Most manufacturer's if they list a continuous torque and don't tell you if it's at stall or at speed, is typically at stall. The rated torque takes into account the spinning (magnetic) losses and thermal (I2T) losses of the motor. At 0 speed, these losses are 0 and thus the stall torque is higher than the rated torqued.
Peak torque is the motor's maximum torque it can output for a short period of time, typically for acceleration/deceleration or overcoming friction. Our motors are rated for 10% duty cycle and thus the peak torque is 3.1 times the continuous stall torque.