The icons on your desktop will just be shortcuts to the programs, not the programs themselves. If you want to check, right-click on one of them and select Properties. There should be a Shortcut tab, while the General tab should show the file size to be extremely small (perhaps just 3 or 4 Kb).
You don't need those icons on your desktop; if you get rid of them, you'll still be able to access the programs from Start > Programs. (To remove an icon from your desktop, right-click and select Delete).
Alternatively you could tidy everything up by organising your desktop icons into folders. Right-click on your desktop and select New > Folder. Give it a suitable name (such as 'Image editing', 'Word processing' or Utilities). Then drag relevant icons onto the folder icon to place them inside it. (Double-click a folder to view its contents).
Your desktop icons are unrelated to which programs run at start up. To see those, go to Start > Run and type 'msconfig' (without the quote marks) into the box. Click OK and select the Startup tab. Click to remove the ticks alongside any programs you don't want to run at start up. Click Apply and OK. Restart your PC. You'll see a box telling you that you're using Selective Startup. Put a tick alongside 'Do not show this message again'.
Alternatively, it's a little easier to control your startup programs if you install Ccleaner:
http://www.piriform.com/ccleaner
(Click on Tools > Startup).
Chris