A capacitor and a battery both store energy, but they are only superficially similar. A battery tries to be a constant voltage source, but in reality ends up being more like a constant voltage source in series with a resistor. A capacitor is nowhere near a constant voltage source. battery stores energy in a chemical medium, while a capacitor stores it in an electric field. Now you could argue on deep principles that the chemical medium is just storage in the position of electrons in the material, but as we commonly understand it they are quite different.
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