It is exactly the same zero gravity as you experience in a plane paraboling to Earth. It 's a bit different from the gravity you experience in far-from-mass gravity in outer space though. In the ISS gravity is nearly zero at every point. But not precisley (though it is not easy totoy measure if not impossible). TheThere is always a gradient giving rise to tidal forces. This is a global force. It It only exists for two separated locals (ponts). Two point masses in the ISS will eventually separate. There is always a certain point in the ISS though for which the gravity is exactly zero. Somewhere in the middle of the ISS. This is happening in a falling elevator too. Somewhere inside the falling elevator the force of gravity is exactly zero. If you place a pont mass in the middle of the elevator it will stay put. If you place it nearer to the bottom or the ceiling of the elevator the force will be still zero but it will accellerate to the bottom or ceiling because of the tidal nonlocal force. You can also say that the ceiling, the bottom and the entire lift exlerience a tidal force and not the mass, which is experiencing no force at all.
This is how you can discriminate between a freely falling elevator and one in free space (or between a lift stationary on Earth and one accelerated in space). In the falling frame (or your falling body) the is always an experience of tidal forces (which are electromagnetic, strong, or weak in Nature).