We could call them power capacity and energy capacity. This system can deliver 2000MW for four hours, or 1000MW for eight hours, but can't deliver 4000MW for two hours, because that exceeds the power capacity.
What are our power sources available to the grid today? Nuclear, Hydro, Energy Storage.
What are the capacities?
Nuclear capacity is 1 GW
Hydro capacity is 1 GW
Energy storage capacity is 2 GW
The battery energy storage is 8GWh with a power capacity of 2GW. There is no such thing as a power storage capacity, because power is a rate. However, the storage may have a power capacity. pedantic, I know.
Watts are joules / second, so watt * hours cancels time on both sides, it's just energy. Watt-hours are more convenient than "raw" joules only because we tend to be more interested in how many hours a battery will last at a given wattage, not how many seconds it will last.
So energy capacity is correct, it's the amount of energy (not power) one can store in the battery.
Edit: I read this as though you were replying to me, not the comment I was replying to. Swimming upstream, I see that, yes, "energy storage capacity" isn't in watts, but rather watt * hours, but I agree with @renewiltord that it's easy to understand once you factor in that journalists, for the most part, never took physics.
The numbers have the units next to them, after all.
We don't state that a car with a 100mph top speed has a 100mph capacity.
The right answer is to use power and energy capacity respectively if you’re talking to lay people but this publication is talking to people who disambiguate based off the units pretty easily.
Nuclear capacity/wind capacity/Energy Storage Capacity. Three different delivery methods for power. That’s how they’d read it at the end of the sentence.
But anyway, the trick is to perform either unit disambiguation or perform one sentence lookahead.
And finally, think of it as no different from using the summation convention in tensor notation. You read it and you’re like wtf but that’s because you’re not the audience and you lack the context to get it.
I think this is where the confusion starts: if someone talks about "energy storage capacity", my first association is the amount of energy that can be stored, not the rate at which that energy can be discharged from the storage (i.e. power).