Activated Carbon is specially treated/made to that the particles have a very high surface area.
This increased surface area of Activated Carbon over regular coal-Carbon makes it much more reactive (more surfact area means more spots for a reaction to take place) and very desireable for use in pyrotechnics and in carbon filtration.
Activated Carbon has a high surface area that allows it to absorb water and other such chemicals from the air. Coal is way too dense for this. However, if the activated carbon has been used to its full extent, it will be about the same thing as the coal.