Somehow I found the Facebook Stackoverflow site, with the icon being the regular Stack Overflow icon with a facebook icon on top of it:
Is it an easter egg? If so, how does it differ from the original Stack Overflow site?
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It is not an easter egg; the http://facebook.stackoverflow.com site is a 'view' on stackoverflow.com, where it only shows questions that have a facebook related tag. In essence, it is the same underlying database, but the question lists are filtered.
From the site's FAQ:
Questions asked on Stack Overflow with facebook related tags. If you want your question to appear here, it must have one of those tags.
The FAQ lists the full set of tags used to create the filter.
The site was created by Facebook in collaboration with Stack Overflow (Facebook's announcement, StackOverflow announcement) to support Facebook Platform developers. When you visit the site without logging in, you are greeted with a message box telling you about the site: