Teams are a special kind of group. The first difference is that a team is bound to an event. In the first instance members are sourced from the "players" who have registered for the event. They can subsequently have team officials assigned from anywhere in the member base. By nature, they have the extended functionality provided by our Team Management tools (ie. Team pages, Team Officials, contact list, etc).
A 'Group' in Majestri is a mechanism to bring together disparate people from across the entire system on an adhoc basis, mainly for communication purposes. They can be made up of anybody, not just players, and their members can transcend events.