Are the iPad 2 30-pin cable and the iPod touch cable different?

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.

The standard iPad/iPhone/iPod Touch cables are identical and interchangeable. As the Apple store item notes:

This USB 2.0 cable connects your iPhone, iPad or iPod — directly or through a Dock — to your computer's USB port for efficient syncing and charging or to the Apple USB Power Adapter for convenient charging from a wall outlet.

However, the chargers are different - as commenter @Mark noted, it takes a long time to charge an iPad with an iPod charger.

iPhone/iPod Touch charger specs (from Amazon):

Input:110-240V 50/60Hz 1.0A, Output:5V==1A

iPad charger specs (from Amazon):

Input: 100-240V 0.45A 50/60Hz, Output : 5.1V 2.1A 10W

The iPad charger can output twice the wattage and current of the iPod charger, so your iPad will charge a lot more slowly if you use your iPod charger (at about a quarter of the speed using the iPad charger). If your iPad is on, it may not even charge because it's power usage is higher than the iPod charger's capacity to charge, as noted in Adam's answer in the question you've quoted.