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Hydro-electric systems store gravitational potential energy. They don't store electricity.
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And batteries store chemical energy.
To the electric utility dispatcher who must plan ahead which plants to run in order to meet today's demand, a hydro plant is just another source of electricity. Its fuel source is a lake instead of a coalpile, and he'd probably think of lake's inventory as megawatt-hours instead of gallons or acre-feet..
"Stored Electricity" is a not bad way to think of a hydro plant, so long as one accepts it's a convenient shortcut and not a rigorous definition.