The Administrators are the owner of GBAtemp, its domain name, its servers, and everything related to it. They make the biggest decisions and do technical work (server administration, domain management, design, coding...).
The Supervisors have access to the Admin control panel of the board (GBAtemp Forum). They mainly moderate the board, but are also involved in the major decisions concerning GBAtemp.
The Global Moderators moderate all the forums on GBAtemp.
The Moderators, also known as Forum Moderators or Local Moderators, moderate categories or individual forums on GBAtemp.
The Magazine Staff are a special group of people who are allowed to post news. They share a private forum with the rest of the staff, but do not have access to the main Staff Forum.
Technicians are members who have total control over the board and servers, but have no responsibilities whatsoever. They don't moderate the board and are not involved in decisions.
The IRC Staffers are a group of people who moderate the IRC channels linked to GBAtemp. They have no moderating rights, and aren't involved in any decision, but share a private forum with the rest of the staff.
For more information on the members, read the IRC Staff members page.