If you look at the gist list for each, you should be able to a get strong feel for these Variations that will help you distinguish them.
Preconditions has a very strong "imposed" aspect -- being forced to follow someone else's rules, play someone's else's game, etc. "Having to take one's younger sibling everywhere" is a great one. Or think of the preconditions Buttercup imposes on the relationship at the beginning of The Princess Bride : “farm boy, fetch me that pitcher”. From some point of view, the preconditions seem dumb, silly, or unnecessary.
Prerequisites focuses more on something being a necessary step.
So it's really the necessary/essential vs. unnecessary/non-essential axis that distinguishes these. However, I feel the gist lists give you a richer sense of the distinction.
Note that like many Dramatica elements, a particular illustration could seemingly fit both. Is a homework assignment Prerequisities or Preconditions? It depends on how it’s presented – where the focus is and where the conflict is coming from.