[billyjmc]

Energy is how much work you can do. Power is how fast you can do it. When you express these in terms of densities, it’s how much energy a certain quantity of material can store, and how quickly that energy can be released from a certain quantity of material.

If you short out a AA battery, it will get warm for a little while. If you short out a 14500 Li-ion battery (which is the same size and comparable energy density), you might get a small explosion as it dumps its energy very quickly.