Aviation is the aspect of aeronautics that practice the art in aeronautics. It coves flying, operating aircraft, maintenance of aircraft, safety management, rules of the air, and so on.
Aviation started around the 18th century with the introduction of a hot air balloon, and in the early 90s, the Wright brothers constructed the first powered airplane.
Aeronautics is a broader term. It covers the entire study of the science and art of flight.
Aeronautics is divided into three major branches which are: aviation, aeronautic science, and aeronautic engineering.
The art and science design and construction of airplanes and aerodynamics are part of aeronautics not necessarily under aviation. The practical theories, navigations, how aircraft are powered are all under aeronautic as a field not under aviation.