No, that's actually megawatts. Grid assets are measured primarily by power, because the grid is operated on dispatch of power.
For storage, the storage capacity doesn't matter from the grid side. Grid operators have an ever-changing mix of resources that bid into the market, and select the winning bids, based on their bid price and power amount, for fixed duration dispatch. When the battery operator is out of power, they drop out of bidding.
If for some reason the energy content is your only concern, and an article doesn't mention the energy capacity, multiple the power quantity by 4 hours. That is the median amount of duration at full power for batteries, due to cost-optimal design. The very first few installations on the grid may be smaller, as in only 1-2 hours, because there's a fair amount of power demand at the beginning for frequency regulation, which requires very short duration. But as more gets deployed, frequency regulation is no longer needed, and 4 hours tends to dominate. I've seen a few 6 hour duration installations too, which may make sense depending on the specific local market needs.
1. How much power output the storage can replace (i.e. discharge capacity) . The appropriate unit for that is watts (or megawatts, etc.)
2. How long can it do it for (i.e storage capacity) - as you point out, the appropriate metric for that is megawatt-hours.
Edit: 1-2 hours of storage seem to be the current state in Texas at the moment: https://www.renewableenergyworld.com/energy-storage/texas-co...
One technical issue with the article, and I see this a lot, is the unit of measure used to describe the storage capacity.
> Texas added nearly 1,500 megawatts of battery storage
In the addled, quasi-imperial units of the US, shouldn't this be megawatt*hours?
I once asked an english person about BTUs, they had no idea what I was talking about. Even though that is an allegedly British Thermal Unit.
Of course, in rational units this would be something like gigajoules:
1.0 Megawatt-hours (MWh) = 3.60 Gigajoules (GJ)