At my school, they offer the following calculus courses:
calculus 1-3
THEN
they also have advanced calculus 1-3
What is the difference between the red and green above?
on the read ones, you will learn all the basics: more on computations; working on at most ; prove some theorems, etc..
on the green ones, you see it is called advanced: here, less computations; more on proving (and prove those theorems you did not prove on calc 1-3); work, generally, on ; and aside from you will also be introduced to other spaces and work on them.
these are just some differences..
I'm assuming this is an American university by your flag. I believe like the above poster said that Advanced Calc is a much more rigourous set of courses. Usually you take Calc I-III freshman year and focus on computations of new concepts and is much more memorization based. After shifting to proof based courses you start from the beginning all over again and analyze the same topics much more intensely and much more generally. The only other possibility I see is some universities have Honors courses that cover more topics and are more difficult, but I doubt this is the way they would title such a course.