system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5: Why, when baking, does it matter if butter is 'softened' or 'melted' isn't it the same thing either way? What difference does it make?
gpt
No, it is not the same thing. The difference is the texture.

When you cream soft but unmelted butter with sugar and add eggs the texture of the semi-solid butter helps to trap air bubbles in the batter, which makes your end product lighter.

When you use melted butter you lose this property, as the melted butter doesn't have the structural cohesion to hold the air bubbles in suspension. 

Butter also contains a fair amount of water; when the structure is destroyed through melting this water is free to combine with flour to develop the gluten and give a chewy consistency to the end product.

This, incidentally, is why cakes not containing butter often depend on whipped egg whites and the support of ungreased pan sides to add that structure.