Can someone explain the difference between this:

∀x((x=0)→∃y(xy=1))

.. and this:

∀x∃y((x=0)→(xy=1))

The top one is in my book. The domain is all real numbers. I understand that it's saying that every real number other than zero has a multiplicative inverse, but I don't understand why it can't be written as the second one? Thank you.