I am pretty sure they are different. The wall part has too "claws" that need to be inserted into the backplate and I doubt the stand version has those. I have the vertical wall mount and there are no inserts for the claws from the horizontal mount.
You can get the individual pieces as spare parts though.
BS9000, BS2300, BC2, BL2500, BL3, Bl2, BS1, BV8, BC4, A8