In Virginia, the General District Court holds a preliminary hearing to determine whether there is probable cause to believe (a) that a crime has been committed and (b) that the defendant committed it. From there, the case goes to the Circuit Court where it is presented to a grand jury. The terminology for the General District Court part of the process is that the case is "bound over" to the grand jury. If the grand jury finds probable cause, then the case goes on the trial docket.

My guess (emphasize guess) is that your "County Court" is analogous to our circuit court. Your district court handled the preliminaries and now it's on to the "real" court, which will probably include a grand jury process. Once the grand jury hurdle is cleared, the case goes to trial, unless the defendant pleads guilty.

These are my guesses.

EDIT: On your second question, the district court will have the records of its proceedings. In Virginia, the case starts fresh in the circuit court.