This is correct and takes me back to a class in the subject at Illinois Institute of Technology. As taught in my time and doubtless today as well, most of "Calculus" is the mathematical field of elementary real analysis, but with a number of accompanying and essential topics, such as infinite series, analytic geometry, and elementary differential equations usually thrown in.
In my day, I took Analytic Geometry as a separate course and three semesters of Calculus before taking later separate courses on Advanced Calculus, Differential Equations, and Complex Analysis. Advanced Calculus is normally distinguished by the presentation of the topological and measure theory basis of modern analysis that are not covered in elementary Calculus courses.
There's really no reason this stuff can't be taught much earlier and I think it has begun to be in some places.
It was at one point the name of a field of mathematics, and it is still the name of a paedogogic tract common in mathematics education, but not a field.