The neutral (white) connects to the neutral bus bar in the breaker box. The ground (bare copper) connects to the ground bar that is a separate bar that mounts to the back of the box. The ground bar is not connected to the neutral bar at all. It is connected via a 10 gauge green wire separately out to the meter box then right to the ground rod. That is the only place the neutral and ground meet, at the meter box and ground bar.
This may well be true on where they connect in your box. BUT, the metal circuit box itself is a complete circuit between the two bars since they will both be fastened directly into the box without being insulated or isolated from the box. Two seperate bars is not uncommon in setups with a lot of circuits---still doesn't make any differance which bar is used.
