When you use water as a heat storage medium, you are storing the heat in the kinetic energy of the water molecules. In common parlance, you are increasing the temperature of the water. Obviously, over time the water's temperature will gradually revert to the ambient temperature, and you will lose all the heat you stored in it.

In contrast, when you store heat in Zeolite, you are not storing it as kinetic energy, you are driving an endothermic chemical reaction that stores the energy in high-energy chemical bonds. After you are done heating the Zeolite to "charge" it, it will return to the ambient temperature, but it still has (lots of) energy stored in the chemical bonds. This energy does not dissipate in the way that the kinetic energy of a high-temperature substance would. The energy can only be released by reversing the chemical reaction, so it is securely stored. You can then transport the Zeolite at ambient temperature to a location in need of heat, and then add water, which reverses the chemical reaction and releases the heat again.

So it doesn't actually store "heat", it takes in heat (i.e. molecular kinetic) energy and stores it in a different form (chemical bond energy).