Why do choc chip cookies change w/different butters?

My name is Chris and my daughters name is Maggie (9yr) She’s doing s science fair project and we have a question we need help with.

Her science project is baking choc chip cookies 3 different ways to see how they change. 1. with melted butter 2. with room temp butter 3. with cold butter

We are having the hardest time trying to figure out why they are changing because of the different butters.

Do you have any idea why? If you have time to field this questions she would really be very grateful.

Thank you so much for your time, Maggie and Chris