I was intrigued recently when playing with TweakUI as to why I had the Internet Explorer icon on my desktop when it was unchecked. I checked the box and now had two icons. The one installed by TweakUI is the one which, when right clicked, displays the Internet Options. The other was a basic shortcut.
You must have just the basic shortcut. However, you can also display the "proper" one by right clicking a blank part of the desktop, selecting Propeties and in the Desktop tab, click the Customize button. Tick the box to display Internet Explorer on the desktop.