It has to be said, no matter whether you adjust the voltage or the current of a motor you are in fact adjusting the amount of power you are applying. However, I do understand that is not what you are asking.
Given a constant terminal voltage, a DC motor, by it's very nature, will consume and deliver an amount of power that will balance the speed and torque ratio.
This happens because as the motor speed increases the back EMF the rotation of the motor generates reduces the effective voltage you have available. That reduction in voltage means the motor will take less current and therefore produce less torque.
As such a balance point is reached where just enough current is taken so the torque balances out the load on the shaft.
That of course is an open loop control system. Apply the power and let it run at whatever speed it settles at. Such methods are good for loads like fans where you really do not care exactly how fast it turns.
In a closed loop system you are really only controlling two things.
1.) Speed: you want the load to move at a specific speed for whatever reason the requirements demand.
2.) Acceleration: How fast the load needs to be accelerated to the desired speed.
Occasionally, you can also add
3.) Position, but you control that by using speed and acceleration.
Some will argue you also want to control torque, but in fact, for practical applications torque is covered, or included in the math, of both of the above. For a known load and a required acceleration, the torque required is simple math. Similarly, for a given speed the load can be determined. Or to put it another way, if you need to accelerate faster or hold a higher speed you need to apply the appropriate amount of additional torque.
So how do you control the motor in a closed loop system to supply the right amount of torque to meet your speed and acceleration requirements?
You basically have two choices, both of which require feedback of the current speed of the motor.
1.) Adjust the terminal voltage applied to the motor.
This uses the motors natural balancing characteristic to find the right speed where the load is balanced.
2.) Adjust the current, and hence the torque directly.
Note: In reality, to adjust the current you effectively apply higher or lower terminal voltage, the difference is really in what you are measuring, not what you are adjusting.
Note I said ADJUST. Except for simple loads where the load itself is linear and well understood, the control variable needs to be continuously adjusted to maintain a stable state despite what the load is doing. Failure to do so can cause run-away conditions or oscillations and often catastrophic failure.
As such, applying a constant amount of power to say a garage door opener would be folly since the load changes markedly between the down and up position of the motor. Similarly, applying constant torque to a load that suddenly reduces, will cause extreme acceleration (assuming the current supply has the voltage headroom.)
This answer kind of got a tad lengthy...
But in brief, you do not control the voltage, current or power of a motor, you control the motion of the motor. You adjust whichever variable makes most sense to keep the motor in a stable state at the required controlled motor movement.