and involves a sphere. Horizon is also used in the phrase "Event Horizon" referring to the "boundary in space-time beyond which events cannot affect an outside observer." ( http://en.wikipedia.org/wiki/Event_horizon ). Because space-time "curve" in the presence of gravity, this term is consistent with the more traditional usage.
A "Classical plane" does not curve, and so the typical definition of "horizon" does not really apply; however, if you are assuming that a plane curves to conform with space-time then the meaning of "horizon" gets a bit complicated for my little brain, and you would need to clarify your question to attract a response from people better capable of answering that.