But we're not talking about cars, we're talking about the electrical grid.

In the current stage of the grid and storage, storage capacity is used not for long duration transmission of energy, but shorter term filling in of power gaps. In the past few years that's been frequency regulation, and now the replacement of peaker plants, or instantaneous response when waiting the 10-15 minutes for a peaker plant to come online.

A watt is a measure of power, not distance. The equivalent unit for a car would be horsepower. You could express the capacity of your fuel tank in horsepower hours. Since both are measurements of power and horsepower is defined in terms of watts you could even measure the capacity of your fuel tank in kilowatt hours. Similarly, you can define the output of your engine in kilowatts.