A short sale simply means the Seller will not have enough money from the sale of the property to pay all costs at closing - including the mortgage(s), fees, and commissions. A Seller can still sell their property for less than their mortgage value and not call it a short sale as long as they stipulate that they will bring money to closing to satify all of their expenses.
However, the most common reference to an advertised "short sale" as you would see it on an MLS listing indicates the Seller has made arrangements with their lender to sell the property for less than the amount owed currently and the lender is willing to allow that to happen. The short sale process can be long and frustrating due to the fact that their are TWO parties on the Seller side which must be satisfied: First - the Seller must accept the offer. Second - the Lender(s) must approve the short sale amount. This is where the offer/purchase process generally slows down. Often a purchase agreement which has been accepted by the Seller doesn't make it to the closing.
Are you planning to purchase a property which is a "short sale" or do you foresee having to sell your own property for less than you owe?