Energy storage modules needs to be measured in (at least) two dimensions: their rated output or power rating, and their energy capacity.
Their power rating, in MW, measures the instantaneous demand requirement they are able to supply. If you add the power rating of all the demand appliances connected to an energy storage module, they need to total up to and no more than the module’s power rating.
The energy capacity, in MWh, specifies the total amount of energy that the module is able to deliver over time.
So what is special about the two?
Well, if you divide the energy capacity (in MWh) by the power rating (MW), you get the duration (in hours, minutes or seconds) that the module can operate while delivering its rated output. This duration is the energy to power ratio. It is sometimes called the discharge time.
For instance, a storage plant with a rated output of 100MW, and an energy capacity of 50MWh, has an energy to power ratio of 30 minutes.
Different energy storage technologies do well in one dimension or another. Some, like supercapacitors, excel at a high power rating for a few seconds or minutes. Others, such as pumped hydro, are able to provide power for a longer amount of time.
Each application has different specific requirements. Often, an essential difference between these requirements is represented by the necessary energy to power ratio: how long do you need to be able to provide power from storage?
Interestingly, when California came out with its AB2514 energy storage mandate in 2013, the bill specified the power (1.325GW), but left the energy to power ratio open.
Ucilia Wang has an interesting discussion on the announcements of energy storage projects in the light of the energy to power ratio. She mentions that utilities announce renewable energy deployments and energy storage projects in MW because they are accustomed to dealing with fuel-based plants whose availability factors are 80-100%, which can deliver energy all year long.
This MW unit is not well adapted to wind or power, or energy storage for that matter (since neither can deliver energy non-stop for the whole year). It might be better to discuss wind and power projects on the basis of MWh/year, and energy storage projects on the basis on MWh.