It's subtle, and sometimes they are used interchangeably. Older English novels sometimes use bind as an exact synonym of tie. But, if you are looking for a distinction, you tie a knot. You bind a wound. So, symbolically, if you are tied to something, you have just a forced connection. If you are bound to it, you are very likely to have an emotional or ither obligation connecting you. But a writer, again, may have no such distinction in mind. https://wikidiff.com/tie/bind