kW is Power output
The power of a car engine or motor is measured in watts, actually thousands of watts, shortened to kilo-watts or kW. A “horsepower” is 746W.
You’ll see “80kW” listed as the power of the Nissan Leaf motor. It’s equivalent to 109hp.
kWh is Battery capacity (or fuel tank capacity)
At First School we mucked about with plastic pots and water, an activity called “Capacity”. anyhow;
The capacity of the battery equates to the size of your petrol fuel tank. The larger the tank the further you can go without filling up.
The original Leaf, for example, has a 24kWh* battery. This means that if you use 24kW of motor power for an hour, the battery will be empty. Or, more realistically, if you used 12kW of power it would run for 2 hours. This will take you, say, 85 miles in mild weather. Similar to two of our English Gallons in a petrol car, I’d say.
So I think there’s a useful (though very rough) analogy between battery size and petrol tank size:
Original Leaf 24kWh, 2 gallons
30kWh Leaf, 3 gallons
40kWh (future Leaf or new Zoe), 4 gallons
100kWh Tesla 10 gallons (however the Tesla uses more energy per mile…)
One nice feature of having more battery capacity is that all of that extra capacity should be useful. I say this because in practise we have a “reserve” of maybe 10 miles, in our minds if not in the real battery. That reserve won’t need to increase with a larger battery.
Since electric cars are more efficient than petrol cars, because they generate less heat and also tend to be more aerodynamic, this analogy doesn’t hold when you look at the actual energy used, (let alone the energy used to refine the petrol – but that’s an argument for another day).
(* In actual fact you don’t have 24kWh available even in a new car, and less still in a 4 year old one! It’s more like 21kWh)