Difference between empty and symmetryPlane
 

I understand when and where to use empty and symmetryPlane boundary conditions.

I wanted to know exactly what the difference were between them. Say you have a mesh with one element thick, would using the symmetryPlane boundary condition instead of empty yield the same results?

As far as I can tell the empty-condition will tell OpenFOAM it should not solve the flow field in the normal direction of the patch is is imposed on.
This is the case when trying to solve 2D (or even 1D) problems with OpenFOAM - which is per se a 3D solver. I'm not sure how this is handled from inside the code.

The symmetryPlane-condition will impose Neumann boundary conditions on the patch it is imposed on.