I have started looking at Facebook in a little more depth - having originally joined purely to be able to assist users in the library (and to that end, joined under a non-de-plume, which I believe broke one of the first rules, but hey - half my friends in show-biz have stage names which they are often known by, in addition to their 'birth certificate/passport' name. I think of it as a useless distinction.
I suspect they got vaguely worried about the MySpace tendency to invent satirical versions of Dubya and Tony Blair, (I found at least 80 God Profiles over there). Still, and all - ID theft for satirical purposes seems like a different threat from the emptying of one's bank account. Um. Tricky, that.
Anyway - it has led me to realize that in addition to thousands of Groups, from the serious to the trivial, you can find another level of Facebook - the Pages.
Pages can represent an individual, like Derren Brown, or an institution like Manchester Library and Information Services, who seem to have mastered the art. Pages can acquire 'fans'.
Groups (open or closed to all except invited members) can form around silly and/or transient issues, or serious and on-going ones. How about the paradoxical group "Let's All Leave Facebook" or a discussion group like "Libraries Using Facebook Pages"
Some discussion of the differences appear on Tim Davies's blog.