It is equivalent to the second, not the first. The first is a completely distinct type -- though you can certainly write a function with that type, given the original function, by uncurrying it.
FWIW, I think the person you are responding to is using the non-Haskell requested mental syntax used by the person who asked the original question, in order so they better understand the semantics (even if at a cost of confusing them for later development in Haskell).