I think you are confusing KW (kilowatt) with KWH (kilowatt hour).

A KW is a unit of power while a KWH is a unit of energy. Power is a measure of energy transferred in an amount of time, which is why you rate an electronic device’s energy usage using power; it consumes energy over time.

In terms of paying for electricity, you care about the total energy consumed, which is why your electric bill is denominated in KWH, which is the amount of energy used if you use one kilowatt of power for one hour.