The G is an AF-S lens, while the non-G lens is not. An AF-S lens has a built-in focus motor, which means that it can auto-focus with cameras that do not have an in-body focus motor. Since the D7000 has an in-body focus motor, it can auto-focus with either lens.

The other advantage of AF-S lenses is that you can override auto-focus and tweak where the camera is focusing by simply grabbing the focus ring and turning it. The camera senses that you turned the ring and stops trying to focus automatically. With the non-G lens, you'll have to actually flip a switch to turn off auto-focus.

The G lens does not have an aperture ring, but that doesn't really make a difference on the D7000 as you can still use every function exactly the same with the non-G lens. You can lock the aperture ring on f/16 and let the camera control it.