Private or Shared reports
Even if shared, only the report creator will be able to edit a report, except for in certain special cases where admin rights have been granted to a specific user.
However, other users will be able to take a shared report as a starting point to create their own Custom Report.
Users can create specific folders in which to place their reports, or they can choose to place them in a general "Unfiled Reports" folder. Neither choice will affect the "Private" or "Shared" status of the reports.