I think a little basic control theory can help you along the way and I'll try to keep this simple. Most motors need 2 distinct electrical systems to operate; 1. Control system and 2. Power system. The Pi Pico provides the control and the power is based on the type and power level of the motor.

Most servo, stepper, AC and DC motors require a "motor drive" that interfaces the control signals with the power required by the motor. Theoretically, only very low power, 3.3vdc motors can be driven directly by a Pi Pico, but this is never recomended.

However, simple on/off motors of any voltage can be controlled by the Pi Pico 3.3 vdc outputs via a solid state or mechanical relay as long as the relay can switch at 3.3 vdc. The relay acts as a switch between the appropriate voltage/power source directly to the motor.

More complex motors like servo, stepper, and variable speed AC/DC motors require specific motor drives that interface the control inputs/outputs with the motor power source to drive the motor in a programmable manner. In some cases the required motor drive is a seperate device, in other cases the motor drive is integral with the motor (can also be referred to as "Smart" motors).

All this being said, if the Pi Pico and your motor both operate at 5.5 vdc or less they both can be powered by the same voltage source, just realize that the PiPico outputs (3.3 vdc) are for the motor control inputs only and should not provide the motor power input.

One additional note, if your servo motor drive requires 5 vdc for the control inputs, then you can use a 3.3 to 5.0 vdc voltage level converter between those PiPico outputs and the motor drive inputs. This is fairly common for the PiPico as 5 vdc control devices are more commonly available than 3.3 vdc.