How do I see the difference between teams from different organizations?
All groups, teams and projects that you are a part of are listed in the sidebar.
Make sure that the group owner adds an organization label to your groups. This way you can identify which groups belongs to which organization.
You can then reorder the groups as you like by drag and drop.
Note: The order of the groups is personal, and doesn't affect the group order for other team members. Re-ordering groups is currently only available on the web application.