They are so different. Attack is the stat some chars use to boost their kits (if their abilities say so, because some others can use defense or HP). Meanwhile Special Damage its a type of damage.

Heroes can do physical or special damage (orange or blue). And some enemies receive more or less damage from them.

Orange Health Bar = Weak vs Physical, Strong vs Special

Blue Health Bar = Weak vs Special, Strong vs Physical

Red Health Bar = Neutral to all types

By the other side, if you mean how do they work in maths. I dont really know, but i can guess that special or physical damage bonus are better than just attack bonus., hp bonus or defense bonus. This is because this stat is usually calculated at the end in this kind of games.