Facebook pages are a businesses official profile on Facebook. Facebook users who follow the profile can get more information on the business like hours, location, mission statement, and in some cases businesses allow for customer service inquiries through the Facebook chat function. Businesses can share images and videos to their page, create events, and access analytics for Facebook posts, like described above.
A Facebook group is a membership based community around a specific topic, product, or theme. Sometimes they are publicly accessible, other times groups are private and require an admin to accept your request to join. Businesses can create their own groups if desired.