Administrator
An "administrator" for a Rust server is a person who is responsible for managing and maintaining the server, primarily by overseeing player gameplay and enforcing the server's rules. The administrator has access to a variety of tools and commands that allow them to manage the server, including adding and removing players, adjusting server settings, and monitoring the server's performance.
The administrator can also use RCON, a remote console protocol, to remotely control the server, this allows the administrator to execute commands, manage players, and adjust server settings without needing to be logged in to the server directly.
An administrator can be anyone, from an individual player who wants to host a server for their friends, to a large gaming community, or a professional hosting company that offers servers to the public.