When I first signed up, I found the groups function here at the forum to be not very user-friendly (hard to search, hard to browse). I haven't tried to use them since.
I suspect (but don't know for sure) that the groups function here suffer from the same difficulties as groups and pages on facebook. What doesn't work about those features on facebook is that if somebody's posted something new or replied to something you've put up, facebook doesn't notify you of that fact. You only know the next time you happen to be at that group/page. Is that the same as the groups here? Honestly I've found it so hard to find groups that interest me (the interface for finding groups is so poor that I gave up pretty quickly) that I have no idea if the forum e-mails you or whatever to tell you that there's activity on your group...
Oh, I forget why facebook's done it- I think pages might have used to have been called fanpages to further complicate matters. I think it's to do with the difference between if you just like something or if you're actually involved in it (business, etc). *or something*.
Groups and Pages serve different purposes on Facebook. Groups are meant to foster group discussion around a particular topic area while Pages allow entities such as public figures and organizations to broadcast information to their fans. Only the authorized representative of the entity can run a Page.