Having just had some problems with cookies myself, and been searching around my hard disk,
I can categorically state that IE and Firefox do store their cookies in different places !!
(Not only that, but IE stores each cookie individually as a file, whereas Firefox merges them all into one text file !!)
Which means that if I say in Firefox "delete cookies", then the IE cookies are still there, and vice versa.
Which means that if I log on to RootsChat in Firefox and then start IE and go to RootsChat it tells me I am not logged in, and vice versa.
Just for fun, the next time I have a bit of time to spare (??) I will load Netscape and Opera and see what happens there.
(I need to load other browsers anyway, because if you have a website, you need to test in as many browsers as possible - after all, you don't know what the "customer" is using !!)
Bob