If you drag a link or favicon on the left end of the location bar onto the desktop to create an internet shortcut then that shortcut gets the icon of the default browser.
If you want a different icon (favicon) then you have to assign that icon yourself to the desktop shortcut (right-click: Properties).
You can usually get the favicon if you append "favicon.ico" to the main domain of a website (e.g. http://www.mozilla.com/favicon.ico ) to display the favicon in a tab and save that image to a folder or see if you can find it in "Tools > Page Info > Media".

I have tried dragging a link on the left end of the location bar onto the desktop and it does give me a shortcut no probs but they all appear the same. ( a white square with firefox logo ) I want the logo of the particular website to make it easy to differentiate each shortcut. I had these before I installed firefox.

Firefox is able to add a specific icon to a desktop shortcut, so you have to do that yourself.
IE can do that as being closely integrated in the OS., but Firefox isn't able to do that.

ok, so how do i do that myself ?

Please read my above post.

You have to find a suitable icon like the website's favicon and save that icon.
Then open the properties of the shortcut to change the icon by browsing to that saved icon.