Energy Density (Wh/kg) is a measure of how much energy a battery can hold. The higher the energy density, the longer the runtime will be. Lithium-ion with cobalt cathodes offer the highest energy densities. Typical applications are cell phones, laptops and digital cameras.
Power Density (W/kg) indicates how much power a battery can deliver on demand. The focus is on power bursts, such as drilling through heavy steel, rather than runtime. Manganese and phosphate-based lithium-ion, as well as nickel-based chemistries, are among the best performers. Batteries with high power density are used for power tools, medical devices and transportation systems.
An analogy between energy and power densities can be made with a water bottle. The size of the bottle is the energy density, while the opening denotes the power density. A large bottle can carry a lot of water, while a large opening can pore it quickly. The large container with a wide mouth is the best combination.