Are the iPad 2 30-pin cable and the iPod touch cable different? They look the same and get mixed up. My iPad 2 can't charge with the iPod's cable but vice-versa works. 

Might this iPad question apply?: Using an iPod charging cable to charge an iPad

Can this behavior be because the iPad 2 30-pin cable and the iPod touch cable are somehow made differently?
The USB-to-30-pin-dock cables are electrically identical. All of them can carry enough charging current for both devices. The same is not true for the power sources as the iPad gets a 10W supply and the rest 5W.

What power source are you using with the cables? iPads need more power than most USB ports offer to charge with the screen on.