False, at least mechanically. The nomenclature is different, and one may have a 1/4" hex slot and the other a square head, but they do the same thing. Not that it matters as the OP has abandoned this thread.
Actually I think that an impact driver supplies both rotational and downward force, while an impact wrench supplies only (and typically far greater) rotational force.
But since this sub-forum is titled The Garage and not The Woodshop, and because lugnuts were a specific application that were mentioned, I don't know why the question even came up.
I did find a refurbished 1/2" C3 impact WRENCH
