Try Opening the properties for each shortcut. Make sure that they are both shortcuts to the same files. If there not delete the one that has a link to files that you don't want. Or try it in safemode! I have never heard of this issue before. I have a Dell Inspiron 6400 with Vista Premium, It could be just an issue with basic!

I'm curious, what programs are those??? Are you sure it is for all the programs you have installed, or just for a few??? Some programs install more than one shortcut on the desktop, wht doesn't make sense it is when you delete one, the other is gone also...