Sigh... No, megawatts does not refer to energy, but rather power, per:
Energy is the capacity to do some physical activities or work, such as running, jumping, etc., while power is defined as the rate at which the energy is transferred, or the work is completed. The unit used to measure energy is joules, ergs and calories. Power is measured in watts. Where 1 Joule = 2.7778E-7 kWh or one kilowatt-hour is equal to 3,600,000 joules.
Put another way: The power of a storage system, P, is the rate at which energy flows through it, in or out. It is usually measured in watts (W). The energy storage capacity of a storage system, E, is the maximum amount of energy that it can store and release. It is often measured in watt-hours (Wh).
The reason why this is important in this context is that an energy storage mechanism (ex. battery) that can provide 1000 megawatts (MW), but only do so for a very limited timeframe (ex. 1 hour) cannot in any way be compared to say a nuclear power plant (ex. 1000 MW) with a typical capacity factor of nearly 93% (i.e. it can deliver that 1000 MW nearly every hour of every day of every month of the year.
Additionally, energy storage mechanisms generate exactly zero energy, but rather just store that energy first generated via another technology such as solar, wind, coal, hydro, gas, nuclear, etc. As technologies like coal, gas and nuclear do not require storage mechanisms while intermittent ones do, in order to fully understand the competitive costs of those intermittent sources, storage costs must be added to them if they ever are positioned to provide base load power capacity.