Is the Main Board that is for sale on the DJI store for Phantom 3 4k the board that goes with the Phantom 3 advanced? I feel like it is most likely for the Standard but it saying 4k throws me off a bit.  

I don't believe so. Your 3 4K is a standard with a 4K camera. The Advanced main board is not the same I am sure of it. If you are confused about the 4K and are thinking of a P3P that is the Pro version and does also have a 4K camera, and it has the same board as the advanced I think. You have to verify the motors are correct though. Some of the Advanced have the 2312 motors which have a different main board than the 2312A motors. You can't swap them around. Not sure what you are looking at for sure on DJI website. It should say what it is for. hope I haven't confused you more than helping. Be careful to get the right one.