Put simply, Competitors are what or who you're evaluating in your competition. It might be teams, individuals, a mix of teams and individuals, objects, groups of objects, etc.
Groups function like tags, and have two functions: to either separate your competitors into subsets, or to match your judges to certain competitors.
In the first case, maybe you have a prize at your science fair for the best elementary level project, the best middle school level project, and the best high school level project. Your Groups would be elementary school, middle school, and high school, and each competitor at the fair would be 'tagged' with one Group.
In the second case, maybe you want your environmental science fair projects to be evaluated by the volunteer judges from the EPA, while you want your model airplane projects evaluated by the volunteer judges from Lockheed Martin. You would have one Group called "Environment" or "ENVE" for short, and give that Group to both the EPA judges and the environmental science fair projects, and you would have another group called "Aerospace" or "AERO" for short, and give that Group to both the Lockheed Martin judges and the model airplane projects.
Check out our other articles on Groups and Competitors to learn more!