Global Moderators are carefully selected volunteers, retired Admins, or members of the team who for one reason or another could not join the Admin team. They are part of the same team as the Admins and relevant Staff members, and are privy to a lot of insider information. They help out in whatever way they can, whether it be translation, tool creation and maintenance, or voting for a group decision. They serve along with the Admins as a valued focus group for opinions and bug-hunting. Global Moderators are not paid, but neither do they have any direct duties that they must perform as part of their job.
Admins are selected from the Global Moderators, and are hired part-time by Twitch. They're not exactly Staff, but due to their close connection with Twitch itself, it's very common for Admins to eventually take positions at Twitch HQ. Admins have varying duties, ranging from shifts of reading and handling reports, taking care of spam, or moderating large events.