How did the airplane get its name?

You can find out your answer through the name itself. The first part air, or aero (depending on where you are from), indicates the medium through which you intend to interact. The second part, plane, indicates a flat or level surface. Rather than calling all flying vehicles, "flying machines" or "flying systems" its much easier to just refer to all vehicles that travel through a gaseous substance according to the plane itself. And yes, by those standards, all vehicles that travel on or through water are hydroplanes.