Under Church of England, parish was a geographical area sometimes like a township, sometimes covering a whole county. Parish boundaries sometimes overlapped parts of several counties. From memory, Bristol Parish included part of Dinwiddie County also. Never have seen a good map though.
The Church kept the civil registry for a parish, and collected tithes. Vestry Book is the administrative record. Parish Register has birth, death and sometimes marriages. For deaths, usually not much to identify people so should be careful matching up names to births. Same may be true for matching marriages to births depending on what was recorded.. Lots of Virginia parish records have been lost to fires and time.