Both use electricity from the grid to “store” energy for later.
Tesla's Powerpack stores this as electricity, and Hydrostor stores it as air—which is then regenerated into electricity.
Don't get me wrong, depending on the area and peak usage, I think it is a good idea, but you can have a Powerpack at your house, but not an underground storage cavern system...Yet.
I produce a high volume of heated compressed air. I must be valuable.