Not really the same thing. Aerospace engineering is really divided into astronautics and aeronautics. Aeronautics being the study of craft (or more basically fluid flow) within the earth's atmosphere, and astronautics being craft outside of the atmosphere.
So if you were to find yourself in a truly "astronautics" program, you'd be focusing on orbital dynamics/mechanics, orbital decay, multiple reference frames, and probably reentry and insertion (along with a slew of other fields like propulsion systems, radiation shielding, bla,bla,bla, etc)
In all likelihood, though, the only way you'll study in astronautics is via a program in aerospace engineering(or aeronautical as many schools offer the general "aeronautics" and then offer foci in astronautics in the higher level courses). As astronautics is generally upper level, and is a more specific field of aerospace engineering. You'll learn all of the core material for aeronautical engineering, then come time to choose a focus, depending on what the school offers, you'll have your chance to get into the astronautical stuff.
The difference only really becomes apparent toward your final semesters, and is generally only different once you get into grad school.