They are indeed the shortcut icons, and they both summoned up the full program when clicked, even after I "uninstalled" one copy by using Revo Uninstaller, as mentioned earlier. Neither copy showed on Revo or the Vista uninstall page after that.
However, some progress has since been made, I'm happy to say. I finally realized I hadn't used the search function under the Start button, and voila - I found a listing for Recuva's Program File. I then deleted that entry, and one icon + program disappeared.
Thanks for illuminating the point about 'target.' I had never before used the Right Click for that purpose.
Now here's a (sort of) tip for you, hazelnut! Right after I bought this laptop and decrapified the junk HP had loaded it up with, I stumbled upon a utility that removes the "little black arrow" from the Desktop shortcut icons. It's still running on my computer, but I'll be damned if I can remember what it's called. If you like, I'll try to hunt it down if you want to try it. I installed the utility because that 'little black arrow' is often an ugly blemish on an otherwise nice-looking icon. Just esthetics, that's all.