This has been my experience, though others might have different ones - if the only change being made to your reservation is the price (no actual flight changes) and the new fare is an internet special, you'll have to cancel your old fare and rebook at the lower fare. When you rebook you'll enter in the confirmation number of your cancelled fare to use as a credit. The remaining money (the amount you saved by rebooking) will remain as a credit to you, that you can use for future travel in the next 12 months from your original booking.
If you're changing something other than just the fare (ie date or time of travel) you can make the changes online without cancelling the original fare. Just go into the Travel Center and choose to Change Air Reservation. The money you've saved will remain as a credit to you, that you can use for the future travel in the next 12 months from your original booking.
Occasionally people have been able to get that credit extended beyond 12 months, or get the amount refunded to their credit card. If you need to do that just call 1-800-IFLYSWA and hope for the best. I've never been able to do that before, but haven't really needed to either since I travel a couple times a year.
I've never used a Ding Fare, but I assume it would work the same way. Hopefully someone will explain their experience with that to you soon.
Have fun!!