They are the same thing, IMHO. I think Wheeler just coined the term Geometrodynamics to emphasize that in General Relativity the geometry of space-time is a dynamic entity.
I might be wrong, but I think geometrodynamics is not just a different name for general relativity. It was supposed to push the idea to the limit and geometrize all classical fields, may be even quantum, and give geometrical description of physical quantities such as charge. Hence the "charge without charge" and so on motto.