system
Given the following post, respond as if you're commenting on Reddit:
human
At a molecular level, how do softened butter and melted butter interact with dough differently?
gpt
Softened butter is an emulsification.  Under a microscope you would see bunches of tangled fats chains and some milk proteins crowding around trapped water molecules.  When that is mixed with dough, the water from butter remains largely trapped in spherical butterfat cages within the larger "net" of the gluten matrix of the dough.  

More water molecules trapped in bubbles of fat means the dough can expand more when the water turns to steam without bursting through the gluten as quickly. Thus your bread should rise more in the oven and youll have larger holes in a softened crumb. 

(Things without gluten or less gluten or with baking powder instead of yeast, may have effects thay can vary widely from a loaf of bread.)

When you break the emulsification butter acts like... well, oil and water.  The water molecules will still eventually turn to steam in the oven but because there is less of a "structured" buffer of butterfat surrounding gaseous water molecule and the gluten, it can more easily escape and the gluten is less likely to stretch as far without butterfat as an "organized" buffer to form an expanding pocket.