The element commonly used in light bulbs and batteries is tungsten and lithium, respectively. Tungsten is favored for its high melting point and ability to emit light when heated, making it suitable for incandescent bulbs. Lithium, on the other hand, is integral in rechargeable batteries due to its lightweight and high electrochemical potential. These elements are critical in different applications; while tungsten provides illumination, lithium powers our modern electronic devices.