You won't get charcoal if you stack wood in a mound, drop in a match and immediately cut off the air. It has to heat up first. Thus, you begin by allowing to burn normally for a while, and then you cut off the air. GMT Serendipity found the following site describing a modern recreation of the Clamp making process in England in 1992 at a Windermere living history exhibit at Brockhole in Cumbria. Only the monks at Margam actually dug for it, from about 1054.
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.