Can anyone define and clarify for me the differences between reissue, repress, and re-release?

To my knowledge all three are largely synonymous. A repress may suggest a more immediate, similar quality to the original release, though, i.e. another batch of copies, but I'm not sure on that one. I'd stick with "re-release" and "reissue".

"Repress" generally refers to a renewed quantity of releases when the earlier one ran out - often by the same label that released the original. Reissues and rereleases refer more to differing formats/tracklists, and labels and distributors releasing them.

Just put "rerelease" if you're not sure.