These are pre-approved Short Sales that were originally FHA financed loans.
HUD sales are foreclosures being handled by HUD. They require an online offering system which requires you or your buyer broker to be registered with them and to have a registered users number. It's actually a very awkward system and serves little purpose other than to waste time, increase blood pressure and probably results in lower sales prices for Government owned property in the long run. As a taxpayer it's hard to say, "Yay HUD"
REO or Bank owned foreclosures are identical other than for the offering process which typically is the same as making an offer on any other property except for the fact that it's being sold "AS-IS" and you will be given a very short time in which to conduct your diligence. You'll also get a limited warranty or special warranty deed which in and of itself isn't a big deal as long as you're able to get Title Insurance. One your offer is accepted the bank will send you a written addendum to the contract which if you read it all the way through you'd reasonably ask yourself, "Why would I ever sign this" all I can tell you is I've seen dozens if not hundreds of them over the years, their all basically the same and if you're going to buy a foreclosure you're going to sign it. Trust me you aren't being treated any differently than any ther buyer of Bank owned property.
Short Sales are when a seller is trying to sell their property for less than they owe the bank. This ale must ultimately be approved by the lender ans well as any other person or entity that may have a lien against the property. Any one of them can refuse and then there's no sale. Many agents who list short sales as well as the Sellers have no idea what their doing and most Sellers will not be approved for a short sale. A lot of time and energy can be wasted pursing short sales. If you are going to pursue them look for short sales that are marked as being pre-approved by the lender, otherwise be prepared to wait 3-5 months for an answer and be prepared to get a NO.
My best advice is to find a good buyer broker in your area who in addition to handling traditional sales, is experienced with dealing with foreclosures and short sales. If they have SFR after their name this is a professional designation as a short sale and foreclosure resource or specialist. I've attached a link to a recent post on Trulia on how to find yourself a great Realtor.
Good luck and happy house hunting.
Just to make this more clear, I'm going to answer out of order...
A short sale is general term, in plain english refers means that the home is worth less than the owners owe on the mortgage. The term comes from the phrase that in order to sell the property, they owners will "short" the bank on what they owe. Short sales are used to AVOID foreclosure, so the owners are in pre-foreclosure. Pre-Foreclosure is when the bank has started the legal process of taking back the home but has not won it's case yet. Therefore the owners still technically own the home and have every right to sell it.
Bank owned, is another general term, that refers to any property that the bank actually owns. Also known as a Foreclosure, or Foreclosed Home, or REO (real estate owned... by the bank). This is what property is known as once the foreclosure has gone through and the owner has lost the home. Those homes go back to the bank as the new legal rightful owner, and are thus "Bank Owned".
HUD is a governmental agency that is linked to FHA, they do lots of things... but for your purposes they take back homes that had FHA loans on them. So HUD homes are foreclosed homes that at one time had an FHA mortgage on them.
Same with Freddie Mac and Fannie Mae homes, these are also govy agencies that have foreclosed homes for sale.
Hope that clears that up for you. All these types of properties are my specialty, so should you have any other questions don't hesitate to reach out to me directly.
A 'HUD home' is owned by the Department of Housing and Urban Development (HUD); it means the home was insured by the Federal Housing Administration (FHA) and they foreclosed when the homeowners were unable to meet their mortgage obligations. You can see HUD owned properties on their website - http://www.hud.gov'. 'Any licensed realtor can show you HUD owned properties. 'Bank Owned' means just that; the bank holding the mortgage foreclosed on the mortgagee and now owns the property. Very often they are listed in the MLS. A 'short sale' is an entirely different situation. It means the homeowners are trying to sell the property for less they owe on it and must get the bank approval of any potential sale. You can often get good deals when buying HUD, bank owned, or short sale properites if you've got the time and patience to look around and have an agent who is willing to work with you. It also pays if you have 'handyman' skills, especially for HUD properties. Hope this helps!