Difference in cookie texture if we use melted vs softened butter I would like to know the difference in the final result if we use softened butter or melted butter in an ordinary cookie recipe. 

A few days ago i baked chocolate chips cookies i waited for the butter to get the room temperature and then i smoothed the butter with the mixer (...) and at the end i put the cookie dough in the frighe. I just wondered what if i melt the butter so i will not have to wait for the butter to get soft, anyway i will put the cookie dough in the frighe later. But what will change? Some recipes demand for butter in room temperature softened and to turn sugar and butter mixture into a fluffy outcome. Some other recipes demand to melt the butter and sugar in low heat. 

What is the logic behind what each recipe demands? And why?
There are many factors in play such as the type of sugars, amount of eggs or other sources of hydration, amount and type of leavening and so forth, but as an overall generalization:


Melting the butter will lead to chewier cookies
Creaming colder/room temperature butter with sugar will lead to cookies with a higher, more cake like texture.
Refrigerating the dough before baking will help inhibit spread because the butter is colder, and takes longer to melt.  It is also gives time for the liquid in the recipe to hydrate the flour.   See What does an overnight chill do to cookie dough, that a 4 hour chill doesn&#39;t?


See the transcript of Alton Brown's Three Chips for Sister Marsha episode for a good treatment of chocolate chip cookies and their variations.