In a short sale, you sell your property for less than the balance of the loans against it. The problem is that unless the lender(s) will accept the proceeds of the short sale as payment in full, you are liable for the deficiency - the shortfall between the sales proceeds and what is owed. With a deed in lieu, you simply hand over title to the bank in exchange for forgiveness of the debt. Most lenders will not accept deed in lieus because they take the property's title with any encumbrances it has on the title. It doesn't want to take a chance that it is taking title to property with undiscovered liens. It is safer for the lender to foreclose, which wipes out all junior liens.
I understand your reluctance to ruin your credit, but sometimes foreclosure is the safest way for you to go: in most cases the lender cannot pursue you for any deficiency (I don't know enough about your situation to tell you whether your lender could pursue you), and these days it is taking most lenders much longer than usual to actually sell foreclosed properties and evict the owner or tenant. I have heard from some folks who have been in their homes over a year without making a payment. You can save a lot of money on mortgage payments during the time it takes the lender to complete the foreclosure and sell the property.
Having said all of the foregoing, you really need to speak with a local real estate lawyer, and possibly a bankruptcy lawyer to fully explore the pros and cons of each course of conduct for your specific situation. There are undoubtedly details about your situation that can't possibly be addressed in this brief summary of options. Good luck to you.