Ok, this is probably, a really, REALLY dumb question, but some YouTube videos showcasing characters combos refer to them as counter combos. Are these combos that can be started after a counter hit? Or does it refer to the combo counter?
Counter hit. Starting a combo with a counter hit subtracts Undizzy from the opponent (15 for light normals, 20 for mediums or a special move, 30 for heavies) (It's late and I'm not thinking straight, Liam has the right numbers), and that can result in negative Undizzy if the gauge is already empty. So counter hits can allow for longer combos that are only possible this way.
also any counterhit does do a bit more damage than it normally would. So there is a difference in damage.
25* 50* 100* Starting a combo from a heavy is important. It gives you an extra 100 undizzy for that combo for a 340 undizzy combo, and the initial hard hitting move deals an extra 50% damage. Here's a video talking about punishes: