The major difference lies in the fact electrochemical processes aid batteries in storing energy and capacitors require no such process hence the rate of release of energy is higher for capacitors. The amount of charge that is stored on plates directly determines the amount of energy stored by the capacitor. The non-involvement of chemical reactions in the storage of electrical energy makes the release process quicker in the case of capacitors when compared to normal batteries. This is also due to the fact that capacitors are known to have very low internal resistance.
Parallel plate capacitors are the type of capacitors that have an arrangement of electrodes and insulating material (dielectric). The two conducting plates act as electrodes. There is a dielectric between them. This acts as a separator for the plates.
A capacitor stores energy in a dielectric dipole in the form of an electric field. Capacitors store energy by holding apart pairs of opposite charges. If a capacitor has very high capacitance, then a small difference in plate voltage will lead to a huge difference in the number of electrons (total charge Q) on the two plates.
A charged capacitor stores energy in the electrical field between its plates. As the capacitor is being charged, the electrical field builds up. When a charged capacitor is disconnected from a battery, its energy remains in the field in the space between its plates.