Not equal! Not even the same substance. Real coal is a mineral that forms underground over millions of years. Charcoal is the chunks of carbon that are left over when you burn something organic. We can analyze these remains to find information about the original substance, but you won't see something like a poisonous tree making poisonous charcoal - what comes out of the fire isn't the original wood anymore.

Even coal-coal isn't all the same. The hardness and percentage of impurities means it burns differently, so certain grades of coal are better for power plants vs industrial use. Go to any coal mining town in Pennsylvania if you're prepared to learn a lot about the superior qualities of anthracite coal.