Energy vs power: what's the difference?

Power is how fast energy is being used. Energy is the total amount used, once you account for how long it ran. A 2 kW heater draws energy at a rate of 2 kilowatts, and leaving it on for three hours consumes 6 kilowatt-hours. That second number is what appears on your electricity bill, because you pay for the total and not the rate.

A tap filling a bucket shows the difference. Power is how far you open the tap. Energy is how much water ends up in the bucket, which depends on the opening and on how long you leave it running. So a 2 kW heater for three hours and a 6 kW heater for one hour cost exactly the same, because both put 6 kWh into the room. Why are appliances labelled in kilowatts when the bill arrives in kilowatt-hours? Because the label describes the rate at which the appliance consumes energy while it is on, and only you know how long that will be. The distinction decides more than the bill. A phone battery is rated in watt-hours because what matters is total charge, while a kettle is rated in watts because what matters is how fast it boils. Electric cars quote both, and they mean different things: kW is how hard it accelerates and how fast it charges, kWh is how far it goes.

Speed and distance work exactly like this. Sixty miles an hour is a rate and tells you nothing about where you end up, because that depends on how long you drive. Two hours at sixty and one hour at a hundred and twenty both leave you a hundred and twenty miles away. Power is the speedometer reading. Energy is the mileage. A fast car does not automatically go far.