As you, I am not an electrician...
Metal back boxes usually have a fixed lug (as well as an adjustable one), in which to screw the accessory into.
This fixed lug (and the screw connecting it) is sufficient to earth the back box (if the faceplate is metal, or the accessory is a socket).
The back box isn't required to be earthed independently, but it is considered good practice to run a flying lead between the two.
If the faceplate is plastic, the earth wires should be connected into the terminal on the metal back box (many plastic boxes also have a suitable terminal).
As opposed to what has been said above - I would run the primary earth wire to the place with the greatest risk, i.e. with a metal switch plate, I would run the earth to the switch plate itself, rather than having a flylead to the plate, from the back box.
Thank you. Is there definitive guidance on the back box not being required to be earthed independently? What in the case of a plastic faceplate?