The biggest difference is time. With a Foreclosure you will hear back on your offer within a week. With a Short Sale you are looking at a waiting period of upto 3 months. Fha, Dva and Hafa short sales are preapproved short sales in which you will hear back in about a week or so. The short sale time frames were getting better last year with about a 30 day wait but this year they have been back up to 60-90 days depending on which mortgage company your dealing with.
There are also a ton more differences between a Foreclosure and a Short Sale if you are on the listing side of the transaction. For most a short sale is a better way to go in terms of credit and future buying power. A common myth is that if you are doing a bankruptcy then what difference would it make to do a short sale. Huge! According to Fannie Mae guidelines if you do a bankruptcy and a foreclosure there are many, many stipulations on future buying power. If you do a bankruptcy and a short sale you can buy again under normal guidelines in 3-4 years.
The list can go on forever on differences however i believe those two to be the biggest