melted or softened butter in baking

Softened butter incorporates more readily, and in a different way from melted butter in yeast doughs. Think of brioche, where very soft butter is added in knobs, allowing it to emulsify with the eggs. Melted butter cannot emulsify because, being an emulsion of water and fat to begin with, once melted its emulsion is broken. It's water content (about 18%) is liberated, and free to roam about the dough, developing potentially more gluten than you wanted. Go for softened butter rather than melted, and you'll be happier with the resulting texture - tender, vs. tough.

Does softened butter have the same effect in yeast dough compared to melted butter (i.e., creates fluffier texture due to the air pockets) ?

I have also heard that softened rather than melted butter makes the end product more moist/juicy. Is that true? The only reason that I can think of why this is the case is that if the butter is not melted, less flour would be required to bring the dough to the desired texture... and less flour means less dryness. Is that so?

Oh, great question. Many Italian quick-bread cakes rely on olive oil rather than melted butter or some other oil. And for any quick-bread/cake recipe that calls for melted butter or oil, you're welcome to use olive oil instead for a richer flavor. As for a *tender* crumb, think of it as more *crumbly*. As for the crumb distinction, envision a muffin versus a slice of cake. A muffin is going to be more *crumbly*. Does that help you?

So, to follow up, do melted butter and oil have the same effect re crumb? Is the only difference the flavor. And does anyone care to elaborate on the crumb and what exactly we mean by tight crumb/tender crumb, etc.

Yes! It's all about the crumb. In the creaming method, you're whipping sugar and soft butter together in order to accumulate millions of tiny pockets of air which, in the presence of leavenings, heat, and moisture, expand to cause a cake or a cookie to rise. The muffin method incorporates all ingredients in one bowl, including melted butter or oil, and produces a much more tender crumb.