ALL my website desktop icons show as same white FILE icon

When I would create a desktop icon for a website in Windows XP, I'd see an icon that was specific to the site. You know, like the round fox with the flaming tail for Firefox, or the red M for gmail.

But when I drag a url and drop it to the desktop in 8.1 (using Firefox, btw), I get none of the site-specific icons. I see them in my bookmarks list but on the desktop every icon is only the white rectangle that I thought indicated a file, on your computer, not an internet website. What gives? Is this a Firefox thing? Can I create a desktop icon in another way? I seem to recall that in XP creating one was as simple as a right mouse click anywhere on your site and picking "create desktop icon", but that doesn't work in 8.1

I'm an old fuddy duddy, and I want desktop icons as well as bookmarks, and I don't want them all to look the same. I can put up with not being able to do anything about the text color for the names of icons if I can actually have a, hello, different icon for every site.

To anyone who can and will help--thanks.

Smoked

I usually drag the little icon on the left end of a URL in the Address bar to the Favorites toolbar or to the Desktop, not the URL itself. The icon itself relies solely upon a Web site having a favicon.ico file on it somewhere. [I've lost track of it but I used to have a small program that could harvest favicon.ico files and save them but that was back with WinXP and IE6, don't know if it would work with later versions.]

Hey Breton, thanks, and yes that's what I do. However, I have discovered since I first posted that this is an issue ONLY in Firefox and not in IE. In IE I can create desktop shortcuts that have site-specific icons. But in Firefox it is a no-go, just blank white file icons. If anyone has any knowledge of this problem/issue, and has a fix, let me know. Otherwise I will retire to a Firefox forum or site to see what might be learned. Thanks.

Smoked