Set Menu and Course Set Menu names are replicated across all branches in a multi-branch system. However, the contents of each Set Menu or Course Set Menu can be different in each branch.
If you want all your branches to have exactly the same Set Menus AND contents, use the 'Synchronize details in all branches' checkbox in the appropriate editor screen. The screenshots below show the relevant screens for 'Set Menu' and 'Course Set Menu'.
Set Menu
Course Set Menu
If you make create or make changes to a Set Menu and DO NOT tick the 'Synchronize details in all branches' checkbox, you can have different Set Menu contents for each branch. Take care to ensure that the 'Branch' selector drop down list box is set to the correct branch if you want branches to have different contents.