No.On a subpanel, can you wire the ground to an actual copper grounding rod, instead of connecting it to the main panel box?
Is there a specific type of wire you use, or anything specific you have to do?
For the first subpanel in a different building like a detached garage, you need both, an equipment grounding conductor accompanying the feed wires back to the main panel, and the ground rods (two, at least 6 feet apart, and 8' long).
For separate wires strung through conduit, the EGC can in some cases be smaller than the other conductors but I don't have the sizing table handy. For Romex type cable, just get it "with ground".