Power is measured in watts, not amps. You do have only 20A of current for a 2 pole 20A breaker or for a single pole 20A breaker, but your wattage doubles when you go from 120V single pole to 240V double pole. So you are getting twice the power over the same gauge wire.
120V X 20A = 2400Watts
240V X 20A=4800Watts