Let me try to ask this in an understandable way.
Been many, many years since I wired any outlets, switches, etc., so possibly the building codes have changed ? (live in Mass.)
Previously, when you installed or replaced a switch, outlets, or even a GFCI, it was "required" that you run a green grounding wire from the back of the metal box where you would have a screw grounding together the box, and All the green wires from the outlets, etc grounds to the switch or outlet grounding screw.
It was not allowed, I think, to just have the mounting tabs do the grounding thru the box shell, although the mounting tabs were (usually) common with the outlet or switch grounding screw.
I now see that Leviton implies for their their GFCI devices that you can simply use the mounting tabs, and that a separate ground wire to the box grounding screw is not required.
Do I have this right ? Has the code changed.
Just use the GFCI mounting tabs, and don't run a separate ground wire ?