GPX - Can be of two flavors, auto-routeable or breadcrumb. The auto-routable version will guide you from point A to B with on screen pop-ups. Should you get off the route it will adjust the route to keep you moving in the right direction. The breadcrumb version simply displays on the map the path you should be following.
HST - Not compatable with the Edge as far as I know.
CRS - A course file. Contains a breadcrumb path to follow, elevation profile of the path, and potentially the virtual partner info allowing you to race the partner. The newer version of this file type now has a TCX extension.