A white dwarf is the dense cinder of matter left over after a star like our Sun has evolved past its red giant stage, and its thermonuclear fusion can no longer support the weight of its mass against gravitational collapse. The star looses much of its outer layers, and its helium-rich core collapses into a body about the size of the Earth, retaining much of the original mass of the star. The maximum mass of a white dwarf is 1.44 solar masses, beyond this Chandrasekhar Limit, it will continue to collapse into a neutron star. White dwarfs start out their lives very hot, with temperatures above 50,000K and slowly cool over the course of billions of years into low temperature bodies. One of the coolest, and therefor oldest, white dwarfs is van Maanen 2 with a temperature near 4500 K making it an orange, white dwarf!
Brown dwarfs are a horse of a different color. They are stars so small that fusion reactions can not have started in their cores because the temperatures there never got high enough. Jupiter's core temperature is 56,000 K, and brown dwarf stars with masses of 0.04 solar masses ( 40 times Jupiter) barely get to 500,000 degrees. The boundary between a large planet and a small, failed star is believed to be near this mass. They are supported against collapse by electromagnetic forces.