The Pro has better video resolution and more advanced audio noise filters. It also has more advanced motion detection software.
Both the Pro and the plus come with two battery slots and one battery. You do not need a second battery for the camera to work but it is a nice feature to have.
The camera is programed to draw power from one battery and then switch to the second battery when the first one is drained. The app will alert you when one battery is drained. You can then remove the drained battery, recharge it, and put it back long before the second battery is drained. In this way, you can keep your camera online with no interruption power.
A second battery is ususlly priced at about $35.