Gust & bimmer848, your cars apparently act similar to 2011 & 2012 Edges where they did have an "M" instead of "S" in the gear shift indicators. The "Sport" mode was introduced in 2013 & as per the manual, should operate like what members OnEdgeinMA & akirby described.
I believe its that your cars, though 2013 models, are programmed with 2012/2011 softwares & hence the way they operate. It would be nice though if we can program our 2011 to get the "Sport" mode.
Edit: Sport mode is mentioned in the Product Sheet for the 2013 Edge under "New and Notable" (2nd point).
http://media.ford.com/images/10031/2013_Edge.pdf
