Butter Muslin is a tightly woven cloth, much like a flour sack material. Butter muslin is used for draining, pressing, and bandaging both hard and soft cheeses.
Butter muslin is great for draining moist cheeses and soft cheeses, because it doesn’t allow for complete draining of vital moisture and butterfats, and it's good for holding in small, soft curds.
Butter muslin is usually harder to find, because it is really only used for cheesemaking. But any place that sells good cheesecloth will usually sell good butter muslin too, although it might be slightly more expensive. All butter muslin can be washed, dried, and reused as many times as you like, but smells, flavors, and pieces of curd will stick to tightly woven butter muslin more readily than it will to cheesecloth, so you will have to be very diligent in keeping it clean so as not to impart weird or off flavors to your next batch of cheese.
Cheese Cloth is a loosely woven cloth used for lining colanders, making draining sacks, covering air-drying cheeses, making smoking sacks, and bandaging both hard and soft cheeses.