A manager sees the whole project, works on its files through agents, changes Planning and the Rules, asks the project's agents questions in Conversations, opens agent work sessions, runs and configures deploys, reads and writes its databases, changes the hosting and database connections for everyone on the project, and can see a stored password with a code sent to their email.
Only the owner manages the team: sees the list in Managers, invites managers, revokes their access and handles pending invitations. Everything else a manager can do as the owner does, including removing the project for everyone. In Conversations, though, the owner and the managers delete only the questions they asked themselves, never one they received. There is no role to choose: everyone invited becomes a manager, and an owner who wants someone to stop working on the project revokes their access.
An agent never gets more than the role of the team member it works for allows, and never administration, secret management or deploy configuration, whatever the role. What an invited manager sees is explained in What can I do on a project someone invited me to manage?.