In most situations, there's no difference. You'll usually be busy burning through hordes of enemies, and in that case, repeatedly clicking won't do anything other than to make your fingers hurt after a while, since holding a button will execute abilities at the same speed as if you were spamming them with single clicks or button presses.
However, in some situations, the latter can be clearly better. For example, ranged classes can use the downtime between two casts of the same ability to move further away from an enemy, a procedure known as kiting.
Or enemies could be running away in such speeds or weird patterns that it is incredibly hard to hit them, even when manually attacking using shift+skill button. In that case, it might be wasteful to expend your limited casting resources by missing three spells because you just held a mouse button down. Instead, you might want to aim your shots more carefully.
Many abilities will keep your character locked to his position until the animation is finished, and so it also becomes hard to predict when you can move again if you keep one button down. This can be deadly, for example when you're a weak wizard fighting against the ramming bulls in the highlands of Act I. It might save you some walking time and repair costs if you shot once and reacted accordingly.
One probably doesn't have to think hard to come up with additional situations in which manually clicking might be advantageous.