For a DC motor, the speed (RPM) is proportional to the applied voltage.
The current that the motor will take from the supply is proportional to the load.
A motor with no load will take very little current, a motor which is loaded and doing some work will take more current.
The load on the motor appears as a torque on the output shaft, the more load, the more torque.
So to try and summarise:
Set the motor speed by setting the supply voltage, as you increase the load (torque) on the motor, the current taken from the supply will increase. The motor will also slow down a bit as you increase the load, if you need a constant speed, turn up the supply voltage to compensate.
I hope this helps you to understand a bit better.
JimB
Edit, the relationship between speed and torque will depend on what the motor is driving. for example for a fan, I think the torque is proportional to the cube of the speed.