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.

A lot of confusion here between charcoal and coal, which us understandable with their English etymology.

What you asked about is charcoal which is not at all the same as the combustible mineral called coal. Though coal does have a "charred coal" pure carbon corollary, confusingly known as coke

Charcoal is what is used for filtration and absorption, and is simply pure carbon produced by pyrolysis of (usually) woody material in the absence of oxygen. When this is done, all of the non carbonaceous volatile compounds are driven off, leaving pure charcoal.

If the pyrolysis is done completely, then the parent wood has no bearing on the properties of the charcoal, because all of its other components have been removed.

I have cooked quite a bit of charcoal from woods of all types for use in forging and metal casting. And regardless of the starting wood, the end product is the same. Indeed the only difference is the yield, which is simply because of conservation of mass - starting with denser hardwoods allows packing more material into the same space within the retort when compared to a light softwood.

Once cooked, it's all the same.