PB4Y-1 and PB4Y-2 are completely different aircraft. PB4Y-1 is a Liberator, regardless of the variant, so yes, a B-24D and a B-24J are both PB4Y-1s.
Privateers are definitely an upgraded B-24, an increase in armament of 12 twelve .50s. To eliminate the need for the ball turret, the side blisters could be depressed beyond 180 degrees to provide an overlap of fire below the aircraft. The nature of operations of the aircraft (based on the squadron histories I have) was that they operated at low levels during combat operations.
The downside is that they're slower than B-24s, with only a 236mph top speed, but could carry up to 12,800lbs of bombs versus the Lib's 8000.
+1 for Privateer.