M.S.
You can definitely do different shades of paint/stain from one side of the door to the other. It's done all the time.
added: I forgot to mention you paint the edges and faces etc, the same color as the trim in the room it opens into. So for an exterior door the edge with the hinges would be stained like the outside of the door and the edge by the doorknob that opens into the house would be painted like the interior of the door.