I have outside the regular (i.e. non-GFCI) power outlet that you see on the left.
It has a nice double-cover that will keep water out.
I am about to replace it with a GFCI outlet (right of the picture). The GFCI outlet will not accept the receptacle you see on the left, because there is no room for the screw in the center. That space is occupied by the test/reset buttons.
Is there any disadvantage in installing the ordinary plastic cover (bottom right of the picture) to cover a GFCI outlet outdoors? It is vertical and is under a 3ft shed, so it will somewhat be protected from rain.