Members belong to your organisation and can be given access to its projects. Invite them from the organisation's Members settings by email; they receive an invitation and, once accepted, appear in your team with a role that controls what they can do.
Each project has its own team. Add the members who should be able to see that client's inboxes and captured email, and leave everyone else out. This is how agencies keep one client's work invisible to another.
Manage a project's team from the "Team members" link in the project sidebar.
Testers are a lightweight kind of access for people who only need to send email into a project's inboxes — for example a client's developer, or a QA contractor. They can push test messages in without being full members of your organisation.