The difference is implied by the name, one is limited to 4 inputs, the other, has 8. The key is in the shape of the pad itself.
The way you use a cross shaped (4 button) D-Pad for the 5-8 buttons is by depressing two adjacent buttons simultaneously. It's a horribly lazy design, and hard to use even if you have large thumbs.
There are gamepads made by Valve and MS that have D-Pads designed better for 8 way use, and both are very programmable. The Steam controller runs $50, but the Xbox Elite is $150.