How are Pages different from Groups?

Pages can only be created to represent a real organization, business, celebrity, or band, and may only be created by an official representative of that entity. Groups can be created by anyone and about any topic, as a space for people to share their opinions and interest in that subject. Groups can be kept closed or secret, whereas Pages are intended to help an entity communicate publicly.

Pages also allow people to maintain a personal-professional distinction on Facebook. If you're a group admin, your name will appear on that group, while Pages will never display their admins' names. Additionally, when you take actions on your group, such as posting on your group's Wall, these actions will appear to come from you as an individual. However, if you post or take other actions on a Page you own, it will appear to come from the Page.

Groups are generally meant for smaller groups of people you know personally, and have limiting functions in place when the group members exceed a certain number. Pages are intended to be a place for organizations, businesses, celebrities, or bands to connect with users who like them. You can create a Page here: http://www.facebook.com/pages/create.php or create a group from the “Create Group” link on the left hand navigation of your home page.

via Help Center.