It shifts one of them but it doesn't matter which one, The only thing that matters is the way they shift relative to each other (you could shift just one, or you could shift both in opposite directions by half as much). Which one that is actually shifted depends on the device.
Power factor is the measure of how much the voltage and current are cooperating together to produce power. THe more they cooperate the more actual power they produce.
If you don't understand power factor, here is an analogy for voltage sine waves and current sine waves and how their phase relationship affects power:
It's like two people pushing a car that is too heavy for one person to push. If you push together and rest together (in phase) then the car has the fastest average speed. If one person pushes while the other rests (90 degrees out of phase), the car doesn't move at all. If you make it so the periods of resting and pushing slightly overlap between the two people, the car moves will have a slow average speed. The more overlap there is where two people push together (and rest together) means the car has a faster and fastser average speed (until you get to the maximum average speed where the two people always push the car together and resting together).
The two people are Voltage and Current, and the average speed of the car is called power. Pushing is the positive and the negative peak of the sine wave and zero is resting. The actual average speed of the car is the actual power, and the maximum possible average speed of the car is the apparent power. The ratio between actual speed and maximum speed is apparent power.
Remember, there are TWO power values- the actual power and the apparent (maximum possible) power. And the voltage and current are sine waves, not constant DC.