Astrophysics or Astronomy?

I have been wondering about the same thing.  I would say that Astrophysics is look upon slightly higher than Astronomy because Astrophysicists have to be able to do a lot more physics, but both are important.  Astronomy would focus more on the observing and explaining aspect wheres Astrophysics would focus on experimental or theoretical explanations for what we see or think happens in the universe. Most jobs for either will be in the collegiate setting and there you can expect to get a professor's pay which isn't amazing.  You will probably be involved in research and you have to ask yourself if you want to be working with the numbers (theoretical astrophysics) the accelerators and other devices (experimental astrophysics) or with the telescopes (observational astronomy).  You are going to need a PhD no matter what though.

All professional astronomers, and some of the amateurs, are astrophysicists as well. An astrophysicist is a theoretical astronomer, which is a lot like a theoretical physicist. I'd say major in astronomy for your BS, in physics for your MS, and astrophysics for your Ph.D.

Astronomy is a broad, general term for the discipline.  I have a PhD in physics, and I work as an astronomer and a cosmologist.  Astrophysics is a term used to describe the physical attributes of the Universe.  Cosmology is used to describe the study of the whole of the universe, with an emphasis on it's origin and direction.  There are other branches to astronomy such as the study of other planets, and many other specialist fields.  As a cosmologist, I am equally interested in the work done in particle accelerators such as the LHC at CERN, as hopefully, they will give us new insights into the most fundamental constituents of the Universe, whereas a planetary astronomer is likely to be less interested.  Given your areas of interest, I would suggest you major in physics, though math will also become pretty vital.  As to your last question, I'm afraid nobody gets rich in this field, unless they are lucky enough to hit upon a best-selling book.  In fact, a large part of my time is taken trying to raise funding, as is the case for many of my colleagues worldwide.