Hello Archana,

See Aerospace and Aeronautical Engineering are two branches that looks similar, but they are not same.

What you need to understand is that, Aeronautical Engineering is a specialisation feild of Aerospace Engineering. To understand better please go through the following points.

Aerospace Engineering.

• In this branch of engineering, students learn about professionals design, building, testing and maintenance of Civil aircraft, Missiles, Space Shuttle Rockets, Space Stations and other such units. Aerospace is a broad field and also comprises subjects that are taught under the aeronautical engineering course.
• Popular subjects : spacecraft design, introduction to astronautics, spacecraft dynamics and orbital mechanics.
• Scope in India : Aerospace engineers have the option of working in government as well as private organisation. Some of the departments where aerospace engineers can work or Airforce, corporate research companies, Airlines, helicopter companies, aviation companies, defence ministry, aircraft manufacturing, government owned  air services, etc.
  

Aeronautical Engineering.

• Aeronautical engineering is a field of aerospace engineering. It can also be understood as a specialisation of in the field of aerospace. The field of Engineering comprises the study of designing and building aircraft such as aeroplanes and helicopters.
• Popular subjects : Thermodynamics, Heat Transfer, Aircraft structure, Flight Mechanics and Aircraft stability and control.
  
• Scope in India : although there are a lot of opportunities for aeronautical engineering graduates. The opportunities in the court profile or better outside India. Since there are better space centres outside India, the scope of this field is much better once you have pursued Masters from universities abroad. However there are a few government organisations that offer high paying jobs in this field.

So the basic difference between Aerospace and aeronautical engineering comes out as,

aerospace engineering is about  aircraft that operate outside of the earth's atmosphere such as a Rockets, satellites and other spacecrafts.

Aeronautical engineering is all about aircraft that stay within the earth's atmosphere such as aeroplanes and helicopters.