The billing column in standard timesheet displays both Billable or Role Names (assigned to the user) and Non-billable.
The billing column in the standard 2.0 timesheet displays Non-billable and the role is displayed as Billable (with the name of the role in brackets).

Example:
If a user is assigned a role called Development then:
In standard timesheet in the billing column when the user tries to select the role in the drop-down it will be available as Development.
In standard 2.0 timesheet the same role will be displayed as Billable (Development). Check the screenshots attached to this solution.

Standard Timesheet

Standard 2.0 Timesheet