Cosmology and Astronomy
Richard Feynman has nice words about science. It is not bad to read chapter 3 of "Feynman Lectures on Physics". The main point of his lecture is that "there is no strict boundary between different fields of science", "nature doesn't concern what we call its parts!"
So, we can't look for a line that divides celestial works into astronomical or astrophysical or cosmological. Although the main keywords about these fields are respectively: "observation of celestial bodies", "machinery of celestial bodies", "evolution of cosmos as a whole". Surely, they use findings of each other.
Recently, cosmology has encountered with big questions, really big! Dark matter and dark energy are the most challenging ones. But it is interesting that if there weren't astronomers and their numerical data, cosmology could not progress.
Usually the students of astronomy focus on classical mechanics and optical methods to be able to observe celestial bodies. Astrophysicists concern general relativity and nuclear physics as two important tools to describe stars or galaxies. But cosmologists are interested in modern theories too, especially string theory. Therefore the courses which they pass should be related to these subjects.