What's the difference between Physical Offence vs. Special Offence?

Nothing to do with plague or dots. These do percent health damage.

Some abilities say "deal physical damage" some say "deal special damage".

CLS only does physical damage, so never uses the special damage in his stats.

GMY only does special damage, never uses the physical in his stats.

Cody has both physical on his basic and special on his aoe, so he uses both sets of stats.