There is also a meaning that it's a way of preparing leather that makes it white, as opposed to Tanning.
Actually, the distinction is between using vegetable sources (bark, leaves) or chemical sources (alum). Technically, tanning only refers to vegetable sources, but that distinction is rarely made anymore. From what I've seen, now if the distinction needs to be made, the leather is called "veg-tanned."
You're right, though, in that tanning solutions made from bark, etc, stain the skins and make them the characteristic brown color. So if you want to preserve a skin (such as a fur) without staining it, you would taw it.
--Mel