And I am here with answers for you all! There is a subtle difference:
Shiv, n: a slang term for something that can be used as knife.
Shank, n: a slang term for a knife that's typically made from something else. A shank can be considered a type of shiv.
So bottom line is that they are both types of homemade knives. A shiv, though, is usually made from something already sharp, like it can be a razor blade attached to the handle of a toothbrush. A shank, however, would be the end of a toothbrush handle meticulously filed down to a sharp point. Make sense?
Hope that helps. :)