Batteries are rated by what amperage they can deliver. Motors are rated by how much they can accept. Higher voltages will ram more amperage into the motor. Larger higher pitched propellers will cause the motor to draw more amps.

So, it is a combination of motor pull and battery push. You just don't want to exceed the max that either can handle. Having a battery with a higher amp rating does NOT mean that it will push more amps into the motor, only that it can deliver that much if the motor demands it.

If your motor wants 20 amps and your battery can only deliver 15, the motor will not reach full power and the battery will potentially be damaged. NiCd and NiMh can handle the abuse better than Lipos. Lipos get very upset if you try to draw too much.