Depends on who you are talking to. Battery engineers tend to talk about capacity as storage potential (energy). The rest of the energy industry (resource planners, developers, manufacturers, etc.) talk about capacity in power terms (instantaneous discharge.)

When you see people talking about Lithium-based chemistries, you'll often only see power terms because they are almost always for 2-hr projects. Nowadays you'll see more differentiation between 2-hr/4-hr/6-hr storage (and a few interesting companies doing 100-hr+).

Unpacking the headline - A 600MW project of 4-hr lithium is 2.4GWh of storage capacity. The capacity rating of this project is 600MW, the storage capacity (2.4GWh) is an ESS specific attribute.

Another important dimension to capacity is how much accredited capacity your project has. Usually projects are only given credit based on some set of historic averages of how much system load the asset actually serves (e.g. if you for some reason had a battery could only discharge at high noon every day, 200GW of this resource would in a sane world have an accredited capacity of near 0 because it's completely coincident with existing solar.)