Hi James,
It is all to do where they work.
In a grand magasin ( department store) it would be 'chef de rayon' .
rayon = department
In a hotel chef de l'étage.
The term 'manager' is multi-faceted in French.
If it is somebody who manages a shop or a hotel for the owner, the term 'gérant' will be used.
In companies, 'le/la responsable' is the term that will be used for someone who is a manager of a team or a department.
For a project manager, it will be chef de projet.
These can also vary from company to company depending on their size.
Hope this helps!
