Your differentiation between hay & straw is also my understanding. The hog farmer I worked for one summer in HS also farmed wheat. He had the spreader taken off the combine so the straw would make a windrow for baling. The bales were put up in a barn or a shed to be used for sow bedding. This was way back in the 70s before the confinement sheds used today.FWIW, generally speaking, hay is for feeding and straw is for bedding. I think hay usually includes more foliage and straw is mostly stalks, but I’ve never actually baled straw.