Software Engineering vs Computer Science

I am an aspiring Software Engineering(MS) student. I want to know the difference between a software engineering graduate and Computer Science graduate ? What is the role of an SE and what is the role of CS? which among the both have better job opportunities ? or do they both weight the same? what are the jobs that both of the above are likely to get? as SE will I be able to enter the realm that a CS student does? And can a SE apply for a job where it says "B.S., M.S., or Ph.D. in Computer Science or equivalent,"? Thanks