Why is there a difference between softened and melted butter when baking?
Basically, when recipies call for softened butter, they use the creaming method; the sugar and butter are mixed together in such a way that the sugar cuts little air bubbles into the butter.  These little bubbles can add some extra puff to the cookies.

If you melt the butter first, not only do you not have those air bubbles, but there's water in butter, so you'll end up getting some gluten development when you mix in the flour and make a chewy cookie ... but more importatly, without the fat being (near) solid, the cookie will slump a lot more, and spread out before it cooks (assuming you haven't otherwise adjusted the recipe to compensate).

There are cookie recipes that call for melted butter; compare the three recipies from the "Three Chips for Sister Martha" episode of Good Eats; the "chewy" cookie uses melted butter.