Is there a difference between the upstream and the downstream oxygen sensor as far as the part number?

It depends on the make and model of your car.

Sometimes the wires of the downstream sensor need to be longer than the upstream sensor. This would mandate a different part number.

Sometimes the upstream sensor is a "wideband" or "universal" type O2 sensor, as opposed to a "switching" type O2 sensor (which is always found in the downstream position). This would also mandate a different part number.