The words plane and plain have several meanings. Unfortunately, both have a meaning relating to flatness, and this is often the source of confusion.
Confusion arises mostly between plain meaning expanse of lowland and plane meaning a flat surface or a level.
A plain (lowland) is always on the ground. A plane (a surface or a level) is nearly always above the ground...like an airplane.
Therefore, if it's above the ground, it's almost certainly plane.