What he said, but the only
What he said, but the only real difference between shelf paper (thin fire) and kiln wash is ease of use. And in this context, maybe re-use. Thin fire, or any shelf paper for that matter is a one-time use product. Unusally. With careful lifting, etc., you can reuse, but not a great idea. Mix up a good batch of kiln wash, with good application technique and once dried on a smooth shelf, you can go over it with a nylon and get almost as smooth a surface (and often better) as the paper.
Now if you are carving or texturing with the paper, then you already know the results, but it is still usually a one-time use product.