Deed in lieu of foreclosure: one voluntarily gives their home to the lender in exchange for cancellation of their loan
Short Sale: where the lender allows the homeowner to sell their home for less than what is owned
Foreclosure: where the lender takes the home through a court proceeding
Is one choice better for your credit score than another?
No: All of the options come out to be about the same on your credit score because all of these events represent a loan default. Check out this chart showing how each of these items will affect credit scores at different credit levels.
However, lenders may look more favorably at a short sale than a foreclosure.