Electricity is billed by kWh (kilowatt * hour), an unit of energy. A kW is a thousand watts, an unit of power. It's akin to km and km/h. They are not the same.
Thanks for pointing this out and explaining very well.
When people are mixing these sizes and their units, it's hard to respond friendly without starting out like a school teacher with red ink.
Just repeating, and this is the international, or "metric" system (SI):
is measured in watts, and the symbol is a capital W
, 1000 W = 1 kW.
Energy or work
(equivalent or proportional physical thing, usually), which can be seen as power * time, is measured in kWh (k and h should be lowercase), or other units like joule (J) or newton meter (Nm) are sometimes used, but not in this context.
power, for some time, and pay
for that energy used. A battery has a capacity in kWh and can be charged with a power in kW. The power is basically electric current in amps (A) times the potential in volts (V). In this way the power can be compared between electric systems with different potential, 120 V versus 230 V. 120 V requires about twice the current (amps) to be delivered to get the same power as 230 V systems and so on.