Why is an aeroplane called plane?

If you ask an etymologist, you will be told that the English word 'aeroplane' derives from French, which comes from Greek, meaning 'wandering in the air'. (Wikipedia)

'Aeroplane' is a British term, while 'airplane' is American one.

Plane is short for aero- or airplane. But this is not what I am asking or talking about. Because I also notice some other interesting terms, such as monoplane, biplane and triplane. The word 'plane' may actually means the flat wing surfaces.

Most pioneer aircraft were monoplane. There are differet types of monoplane defined by how its wing is level with the fuselage: low-wing, mid-wing, shoulder-wing, high-wing, parasol-wing (Wikipedia)

The first successful aircraft were biplanes which was invented by Wright brothers. It was designed with the wings positioned directly "one-above-the-other," 

A triplane is equipped with three vertically-stacked wing planes.

We also find other terms contains 'plane', for example Main-plane and tailplane.

A tailplane is a small lifting surface located on the tail.