Speaking as someone ashamed at having never taken Calculus, I didn't know there were 3 of them...

In my experience:

Calculus 1 = differential calculus

Calculus 2 = integral calculus and infinite series

Calculus 3 = multivariate calculus

Calculus 1 = regular calculus

Calculus 2 = backward calculus

Calculus 3 = n dimensional calculus

Differential Equations = inside out calculus

Complex Analysis = imaginary calculus

Don't forget: Real Analysis = generalizable calculus

That was my favorite course.

Ahh yes, I enjoyed that one as well, and had a great professor for it!

I remember going back over the derivation and integration proofs while taking Real II and feeling like that was when they finally clicked.

I was working as a math tutor at the time and Real Analysis was actually a lot of help when trying to explain concepts in Calc I and II.

in A levels classes, we have both of the first two and a little bit of the third

First you learn basic calculus. Then you learn advanced calculus. Then you learn how to apply what you've learned to more than one dimension. The second one is actually the hardest of the three.