For more information see, What are the differences between Procore's time modules?
In the past, you only needed read-only permissions to view all timecards in project and company level Timesheets tools. Customers needed a way to prevent employees from seeing each others timecards. The private timecards setting in the Timesheets tool allows admins to set current and future timecards to private, making them visible to only relevant parties.
For more information about how to set time entries to private, see What is a 'private' timecard and which timecards can be set to private?