It is confusing, isn’t it? In some cases we use “energy” or “power” indifferently, and in other cases we don’t.
To be clear: what the electric company charges you for is energy, in kWh. It’s a kWh that costs $$. The rating on your appliance is a power rating, in kW: it defines the rate at which your appliance consumes energy.
In the same way, a generation plant’s nameplate capacity is a power rating in MW or GW, Its output, over a day, a month, or a year, is energy, in MWh or GWh.
I feel the need to mention this because I want to post about the energy to power ratio soon…
I wrote a detailed page on the difference between energy and power here.