What is the difference between Mechanical Engineer and Aerospace Engineer?
If you want to work on the landing gear or passenger seats, a mechanical engineering education is the best qualification.
If, however, you want to work on control surfaces or fairings, an aerospace engineering education is better suited.
While both teach similar basics, the aerospace education is much heavier on fluid mechanics and lightweight design. Having studied aerospace engineering in Germany, I was shocked to learn that master students in Aero/Astro at MIT had no idea how to design a screw connection. Therefore, much depends on the country and its ways of teaching. In the US you will get an excellent education in one narrow field at the cost of breadth. In other countries your education might take longer and give you less expertise in one field but will cover the fundamentals much better.
In general, at university you will be taught how to learn. You will learn the basic stuff which will enable you to read special literature and you will learn where and how to locate resources that help you along. This will be the same in both branches and it depends on you to round out your knowledge yourself.
To quote from an earlier answer:
Take the example of Ed Swearingen: He never went to engineering school, but spent years working with airplanes, gradually moving from handling to repair to improving them. In the end, he was a successful self-employed consultant who helped with a number of airplane designs and created some of his own designs, too.
So here is what I propose to do:

Hang out at a local airport (ideally one with lots of hardware passing through the local repair shops).
Don't shy from getting your hands dirty and from asking questions until you are satisfied with the answer.
Try to find experienced engineers and work closely with them.

Do that for 10 years and you will be hard to beat as an aircraft designer. If you happen to attend University in Germany, be sure to become a member of one of their Akafliegs - that is the best start into an aviation engineering education.
It also helps to build and fly model airplanes. Models can give you valuable lessons in aerodynamics and flight mechanics.