As a general rule of thumb: there is always a transition between "on" and "off".
For your solar cell that means: no light -> no voltage , a lot of light -> maximum voltage, maximum current.
You can try this yourself, if you equip yourself with a cheap multimeter and use this as a replacement to the motor in both: current mode and voltage mode.
You will see changes in your readings, if you change lighting conditions.
When you think about your motor, the same rule applies: no voltage (=no energy) no movement. Rated voltage -> rated movement.
Exchange the solar cell with a standard battery cell (1,5V). It should move.
Add your multimeter in between in current mode.
You will notice, that the current depends on the friction you apply to the motor.
Get yourself a "adjustable battery" (adjustable power supply) to play with the voltage applied to the motor.
You will notice, that you need a minimum voltage to get the motor spinning.
This is mostly always the case in physical systems and called friction.
You have to apply enough force to overcome friction.
In the case of a motor: you will have to supply enough voltage and your energy source will have to be able to supply enough current to start the motor spinning.
If you want to start playing with the motor, without waiting for a adjustable power supply: try to get it running with the battery cell and then add some thin wires in between. You will notice, that the motor speed changes and you will notice some dependence of the diameter, length and chemical composition of the choosen wire.