You can read the in-game description:
Fellow
Every fellowship member can use the fellowship chat, trade with other fellows without a fee, give and receive neighborly help, and send circular messages to all fellows.
Ambassador
On top of the normal fellow rights, an ambassador can invite players and accept invitations.
Mage
On top of all ambassador rights, a mage can expel or change the title of other members (apart from the archmage), change the fellowship profile, and open or close the fellowship for invites and applications.
Archmage
On top of all mage rights, the archmage can disband the fellowship. The archmage cannot leave the fellowship, but can appoint a new archmage- and become a mage.