This is short, but it took me a while to figure out and I’ve not seen it elsewhere.
Facebook offers both Pages and Groups for use by businesses, organizations, sports teams and the like.
Pages are like a multi-author blog. Authorized members can post as the Page (Facebook now shows the actual author name as well, that’s a good improvement) and all followers will see this — though unless you pay per post it may get buried deep in follower feeds.
Comments are associated with a Page Post. Non-Page posts are shunted to a somewhat hidden area and are NOT shared with all followers.
Groups are egalitarian. All posts by all members go to all followers. There are no RSS feeds for Groups.
You can use IFTTT to create a Page or Group entry.
Pages, like blogs, are public facing. Pages can be configured to be accessible to non-Facebook audience (though they will be nagged to join Facebook), and, as noted above, they have RSS feeds. Groups are only accessible to members and members have to be approved by admins.
I’m not sure whether Pages or Groups get precedence in follower news feeds. I suspect Groups get higher rankings than Pages that don’t pay to play, but I’ve not done any testing.
it’s hard to say whether Pages or Groups are better for non-profit organizations. The big advantage of Pages is that they are available to non-Facebook members, but the nags are very annoying. I lean towards Groups for most, but Pages have promotion advantages. For business Pages are clearly better; they’re really designed for business use.