The dry cells have a graphite rod going through the middle and is surrounded by an electrolyte paste which contains NH4Cl and MnO2. The graphite rod is the cathode and the zinc canister is the anode and well as the cell container. The overall reaction is 2NH4 + 2Mn02 + 2H2O + Zn --> 2Mn(OH)3 + 2NH3 + Zn
The "Button Cells" are used because dry cells have a limit to how small an amount of electricity can be produced from it. Button Cells are used to power hearing aids, digital watches and remote locking devices for cars. The Anode is Zinc which is positioned above the KOH electrolyte paste which is above the cathode which is composed of Ag2O and water paste. This is all cased in stainless steel. The reaction is Ag2O + H2O + Zn --> 2Ag + 2OH + Zn
Sorry for no pictures or anything but as I see it the main difference is in the reaction obviously and the amount of power that they produce. Hope this helps a bit