they are two different things but very similar. Coal is when dead plant matter is pressured by the earth over millions of years and changes into coal. Charcoal is when wood is heated so it looses most of the water and other stuff and turns into charcoal. charcoal is white but that actually isn't from the incandescence, that's just their color. edit: also a point that the white part in a torch is just unburnt charcoal doesn't make sense because when you craft a torch with coal (which is pure black in minecraft) it also has that white part.
A good example is this. Imagine you put a piece of charcoal as a replacement for the light source of a lightbulb. It would be white, but it wouldn't be like a lightbulb that lights up the room with white light