There is no difference between and airplane and aeroplane ticket. Aeroplane and airplane both refer to a fixed-wing aircraft. Aeroplane is predominately used in British English while airplane is an American English term.
They mean the exact same thing. "Aeroplane" is the old British English term for what is now called an airplane. You have to wonder if the movie "Airplane!" was titled "Aeroplane!" when it was released in Britain.
