The term pre-foreclosure applies when the lender is attempting to take back the house because the owner has stopped paying the mortgage. You can read a fairly good, but lengthy explanation here on Wikipedia:
Florida is a "judicial" state, so the bank must go to court in order to complete the foreclose process and obtain a judgement order. The home does not have to be considered a "short sale"; where the mortgage is more than the home is worth, thus the terms upside down or underwater. Although, this is common these days with many of the homes in the Tampa Bay market, homes that have "equity" can also be foreclosed on if the owners stop making the mortgage payment. They can also be foreclosed on by an HOA, if the homeowner stops paying their HOA dues.
Buying a home that is in pre-foreclosure is basically the same as purchasing any other house, except that it generally does take longer and you may need the lender(s) and/or owner of the "note" to approve the sale. Either because there is no equity or the lender may have added additional fee's on top of the original amount owed. Generally, theses sales are considered "as is" because neither the lender or home owner are willing or able to make any repairs.
A home does not have to be listed in the local Multiple Listing Service (MLS) to be sold prior to the completion of the foreclosure process. If the house is worth less than what is owed on the mortgage, many lenders want to see the property listed so they know that the property has been exposed to the open market and they can be reasonably sure that the offer is at or near the properties current worth or Market Value.
As with any home purchase, you should work with a real estate professional to guide you through the process. There are too many variables in each transaction to answer easily in this forum.