Your .exe application files are usually stored in "Program Files" or "Program Files86", with a "shortcut" link .lnk icon placed on your desktop, which starts the program in it's "Program Files" folder. That's the "standard" way it's set up. You can store executable files in your desktop folder if you want and you won't have a shortcut icon there.
Also don't confuse system icons, like "My Computer" and "Internet Explorer" which are placed on your desktop but do not have the small arrow of the other shortcut icons.
To make things even more confusing, there are small applets or "tweaks" that will remove the little arrow component from shortcut icons so they appear like regular system icons.
In short, the shortcut link icons on the desktop is how it's done in almost all instances.