Standings is usually being used by Leagues to record Wins, Losses and Ties. This determines who is on top and who advances to the next level or the championship.
The Details aside from the Wins, Losses and Ties will depend on what you have set on the Scorings Section from your League/Division Settings.
Scoreboard is the same as Team records. The updated score per team base on their Wins, Losses, Ties. This corresponds to the Standings Section on the League/Divisions Page.