You are in a situation that is going to require a lot of careful thought before you act. To try to make this simpler, I will start with the end of your question and work backwards.
A foreclosure is where the bank simply takes posession of the house and evicts you. You will lose all of your equity, if any, that is in the home. In the current market, there is a trend of people simply "walking away" from homes in which they have no equity. That process is a "deed in lieu of foreclosure", where you simply tell the bank that they can have the house, and save yourself the court time. In either case, you wind up with no home, and damaged credit.
A short sale is where you have negotiated with the bank to allow you to sell the house for less than you owe. This process can be tricky, as some lenders would rather foreclose than negotiate to save costs. It's best to get on the phone with your lender ASAP if this is the road you choose, as it can be time intensive to have short sales approved. In either of these cases, it's best to discuss matters with a real estate attorney before acting.
There are other options: If you have little or no equity in the house, and your soon to be ex-boyfriend agrees to it, you could buy out his equity in the house, and take sole possession of it. This would allow you to add a roommate (or two, depending on the size of the home) to help with the mortgage, or to simply rent out the entire house, and wait until this unfortunate market (for sellers) passes. If your Realtor is correct, and the current market value for your home has depreciated that much, then there is likely little or no equity left in the property. Talk with your Realtor to see what the home's rental value may be, or figure out if a roommate situation would work, then see if you could get the home's co-owner to "quit-claim" the home's deed to you. You should not need to refinance if you are the only one on the mortgage.
The reason that I bring up the second option is that it will save your credit rating. Being foreclosed upon, in any shape or form, is going to damage your credit report. A short sale, though an option, can be risky, and the bank may foreclose on you anyways if you are unable to continue paying your mortgage. If you can keep possession of the home, and find ways to keep making mortgage payments for a year or two, you should be able to come out the other side in one piece.
As always, make sure to consult with your Realtor, attorney, financial advisor, etc. before making any decisions.
Hope this helps. Good luck!