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The reminder list is whatever you want it to be! Some people use it as a wishlist overflow, and move books from their reminder list to their wishlist as space becomes available. Some people use it to mark books by a certain author so they will remember to look for upcoming books by the same author. It can serve many functions, and it's there to "remind" you of whatever you need--you just aren't put in line for those books. Hope that helps!
If you add a book to the reminder list, nothing happens, meaning that the book stays there until you remove them. By adding a book to your reminder list, you can see how many copies are available.
If you add a book to your wish list though, you are in line to request that book and at some point, that book would be offered to you.
From the Help Docs:
your Wish List is the list for all books that are currently unavailable to order in the system, that you want to request when they become available. (Books that you are only considering requesting in the future should go on your Reminder List.)