SkyEliteServer.exe is the main SkyElite process that executes the web server. It is a command prompt window application that, if used, has to be minimized and closed manually.
SkyElite.exe is the launcher. This one launches SkyEliteServer.exe hidden, creates the icon and context menu in the taskbar, shows the server IP addresses and allow users to open a specific browser or to close the app.
Also, SkiElite.exe handles the actions related to the passed parameters /autoclose or /silent modes, so executing the server directly will ignore described parameters.
SkyEliteServer.exe is not in the manuals because should not be used by users unless indicated for support purposes.
Hope this helps!