Yes, and flakes can be thick or thin, loose or tight, and the bale can be the same. Right now, we have some grass hay that is pretty loose. The horses prefer the alfalfa but the field needs to be reseeded.
The fresher grass hay - Bo pounces on! I use Oxbow, but I use the barn hay as a sort of treat/encouragement to eat more hay. Most of the time I can't use the barn hay anyhow - it's out of the alfalfa field.