Consider the following: you have a space invaders game. The 'hero' has 2 abilities - a normal attack which shoots standard bolts of whatever and a special attack which hits harder. The special attack can't be spammed.
There are a lot of ways to approach it: Number of times it can be used per level. It will use energy which is slowly regenerated and many more, but for our example let's consider that the 'hero' will not have any of those options and that the only possibilities are:
1) The ability must be charged
2) The ability has a cool down.
The question is: "What is the difference to the player when having 1 button per ability and multiple abilities per button?"
Of course, by this point I have to share that our imaginary game is not made for touch screens (Since if it was then it is pretty obvious that you want as little buttons as possible)
What I can think of is that when holding the button to "charge" it will give the player the impression that something strong is going to be unleashed. The downside of this is that this locks down the possibility to shoot the power up in the middle of combat.