I have a BS in Computer Science, I'm currently in a masters program for software engineering. Skipping the fact the software engineering is different from computer science, the main differences are that your work is more focused (no more general ed) and the work is somewhat more abundant and harder. A masters program is only 30 units (one year fulltime).
A PhD is a whole nother matter. I don't know all the details, but there are tests to qualify for a PhD program. Then you have to aply to programs at different universities. The programs can vary greatly, but they will tend towards research for a professor type stuf I beleive.