I was just asking this question and I stumbled on this post for the answer.
From what I can tell after looking a little more, there really isn't much difference.
Like someone else said, the wrench has a square anvil and generally more power than the driver. Also, I don't think you can get an air-powered impact driver - those are all wrenches.
This is where I saw it:
Impact Wrench vs. Impact Driver | Cordless Impact Driver HQ