No... actually it is watts. You get billed by the kilowatt-hour.
You can cut the amp draw in half by doubling volts (Power = Volts x Amps). The savings is not because of the amp draw being cut, but because things are a little more efficient at a higher voltage. You don't have quite as many losses from wire resistance and such.
If it was the same efficiency, you would gain nothing by going to 240V from 120V.
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