Question

Explain The Differences Between Aeronautical Engineering And Astronautical Engineering

Answer 1

Aeronautical engineering is engineering for planes and jets.
Astronautical engineering is engineering for space research

Answer 2

This is a pretty base answer to your question, but is a good start. Anybody else can feel free to expand on this. 

Aeronautical Engineering deals with designing new aircraft that are limited to the Erth's atomosphere and deal with the concepts, components and forces that affect the aircraft. For example, aerodynamics, avionics, materials science and propulsion. 

Aircradt Maintenance Engineering deals with the repair of these aircraft. This can be part specific. 

So in comparison, Aircraft Maintenance Engineering deals with repairing existing aircraft, where Aeronautical Engineering deals with creating new and improved air craft.