These are official Facebook, branded pages accessed and controlled via personal accounts. This is SU's Facebook page. Only admins can post as the page, and they do so through Facebook Business Manger, found at business.facebook.com, or via the Pages Facebook app.
These are recommended only in addition to a Facebook page. All group members can post in the group from their personal Facebook accounts. Facebook page admins can post into the group from the page as well.
Integration Between the Two
You can link a Facebook group to a Facebook page by enabling the "Community" or "Groups" tab on a Facebook page, under that page's settings. You can also post to a group from a Facebook page, if the two are linked.