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REO  is the short form for Real Estate Owned.  The real meaning is the lenders, usually the banks, have taken over the properties and are actually owners of the properties.  When the properties put up to the market for sale, the lenders/banks had already come up to an agree upon for sale price so usually if the buyers offer the asking price, it will be approved.  However, some lenders/banks will still listen to the sale experts marketing strategy, i.e. to ask for a ridiculously low price to encourage strong competition and thus beat up the sold price.  Anyway, the buyers involved usually can close the escrow within a reasonable time like a normal sale.

Short Sale means even after the sold price of the property is still too short to pay the mortgage.  In this case, the individuals are still owners of the properties and not the lenders.  However, since the homeowners cannot bring additional money to pay back to the bank/lenders, the sold price has to be approved by the lenders.  Since in this case, it is the homeowners who initiated to sell the property to avoid foreclosure, the lenders/banks involved had not yet came up to an agreed upon price prior to the property put for sale in the market, every offer has to be reviewed by the lenders/banks involved.  Thus it usually takes a much longer time for closing.