Actually it is the server's configuration which determines whether or not to serve index.ext in any given folder if it has one when no file is specified. And it is the server config that determines what do if there isn't one. It can just show the directory listing, or a permission denied, or a file not found. It all depends upon the server's config, the browser has little to do with it, all the browser does is request the folder.
The /favicon.ext is another matter. The browser (if so programmed, as most are these days) actually requests that specific file.
Now are you beginning to see the difference?

