Approve are your tournaments that have been approved by the admin and have met the requirements given by the admin. In categories Approve also consists of 7 menus including: Approval, Upcoming, Registration Open, Registration Closed, Ongoing, Completed, and Canceled.
Request are your tournaments that are still waiting for approval from the admin. On category Request this admin will see the details of the tournament and what conditions you have met. In categories Request it also consists of 3 menus including: All Requests, Waiting for Approval, and Rejected.