Depending on your DE, you can have those no problem. You just symlink to the respective .desktop file for the program you want to run. So for example, if you wanna start Firefox from your desktop, you'd look for a file called Firefox.desktop on your system (probably living under /usr) and symlink to that from ~/Desktop.
hmm. I have to admit I don't understand the difference. on windows it's the desktop folder, plus a few separate icons to system utilities with some way to filter them. did you mean that?