For many new Facebookers, thats a great question, but more importantly marketing and branding executives at large companies need to know the vital differences between a Facebook Page and a Facebook Group. In the link given below, Howard Greenstein’s article about Facebook Groups and Facebook Pages explores all various similarities and differences.
One primary difference that is very important for companies to know is this: A Facebook page can ONLY be created and maintained by the company/organization or by anyone else who has been fully authorized by the company/organization. Unofficial and unauthorized Facebook pages can be reported to Facebook on their website. This is important because bad elements could sometime make fake Facebook pages representing a brand, product or service and give out incorrect or misleading information about the brand, product or service.
On the other hand, a Facebook Group can be created and maintained by anyone, so even fans of a service or product can create a Facebook Group.