Difference between a Down spacer and a Fixed spacer?

A fixed spacer and also decrease the distance, not just increase, like a down spacer
Up/down spacers allow for a minimum distance, the actual distance can be larger, a fixed spacer is just that, fixed

Think of a down spacer as one that says "I need at least this much space". So if a page would otherwise be crowded, it adds the space. It doesn't say it needs exactly that much space - so if the page happens to be more closely spaced, it won't put the next staff closer. That's the job of a fixed spacer: to set a precise space, not just "give me at least this much".

Both have their purposes. There are certain cases for which either might work, but most of the use cases for one, the other other would not work for.