Would you say this intro course is a prerequisite to taking the applied course linked by OP?

I've worked through the entire Paar book (which is excellent), and I've made a number of attempts at getting through Boneh and Shoup (which is also excellent). I will say that there is a good overlap in content, but the Boneh/Shoup is solidly graduate-level, whereas Paar is a good and solid introduction for an undergraduate student.

After looking into the TOC of A Graduate Course in Applied Cryptography, I would say the contents of these two are pretty similar to each other.

No, the textbook is much more focused on rigorous security definitions and proving security of primitives against these definitions.