Is it amp or volt switching on ESC that changes speed

Just same basic electrics:
Current is drawn from the source. Not controlled. So if your motor wants 30A, it would want to draw that from the ESC and battery pack.So your ESC and pack must be able to deliver.
Voltage controls your speed, and it is done with impulses send to motor. This is called voltage chopping (Ratio between applied voltage pulse VS off voltage pulse) The wider the applied impulse, the higher the voltage and the faster your motor will spin.
But the more voltage you give (wider impulses) the more current the motor would want from the supply.

Very simple explanation (A bit more complicated than that), but simply put:
Current is what the motor asks from your supply. And Voltage controls the speed by pulsing voltage to motor.
Always go for Max current your motor ask and what your controls can deliver.

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