Charcoal burns quite a bit hotter than wood, and with less residue. Charcoal can also be burned with a draft. When I first started blacksmithing years ago I attempted to supplement my meager supply of coal and coke with a pile of wood I happened to have on hand. I quickly discovered that if you put wood in a forge and blow air through it you will obtain a huge cloud of smoke. The wood will also begin to explode since the water trapped inside rapidly turns to steam.
Charcoal works just fine in a forge or furnace.
The process has since been automated, but you still pay for the energy needed to run charcoal-making kilns. Not necessarily in the same place. A very common occupation throughout period and right up to the beginning of the 20th century is Charcoaler. This is a person who buys or gathers wood, and starts a very controlled burn of it, usually while it is also buried to convert it to charcoal. The wood was often stacked in a very particular order, to allow just the right amount of air to flow through as it burned, and then the stack was lit in the center, and covered with earth a foot or more deep, with the exception of a smoke smoke vent in the top.