In object mode, using 'closest', whether it be for face snapping or even vertex snapping, uses the closest vertex of the bounding box around your mesh, not the mesh itself. You can view the bounding box of your mesh in the object properties submenu, under viewport display.
So, what happens is that when you rotate a mesh in object mode, the bounding box rotates with it. However, in edit mode, since you're editing the mesh itself, the bounding box expands in one or more axis, without actually rotating. So when you go ahead and try to snap using closest mode, you'll actually be trying to snap with the closest vertex of the now expanded bounding box.
I highly suggest you play around with it and view the bounding box of your mesh to really understand what I mean.