As I understand it, evidence rules govern what you can or cannot put before the fact-finder at an actual trial. They don't govern the acquisition or handling of evidence by law enforcement.

Well, all of that, to some degree. Most of evidence revolves around admissibility, trial objections regarding admissibility, motions (typically the motions in limine I mentioned to admit or exclude evidence), etc.

As AnnaD mentioned, rules and practice regarding hearsay evidence and its exceptions is big.
Once you get all the big rules down, you get to go into state distinctions, which is big fun. (e.g., admissions are not hearsay under the FRCP, but are admissible under an exception in the Cal. Code of Civ. Proc. Rules of privilege, and which conversations are privileged differ, etc. It's all great bar exam fodder.)

Discovery probably won't come up in an Evidence course very often, unless it's about methods of discovery and whether they're sufficient to prove reliability, but even that's probably on the outer edges. Most discovery issues will come up in civil procedure or in dedicate discovery (and more and more, e-discovery) courses.