Boeing patented the flush system on the aircraft.
They use a vacuum pump, until above 15,000, then it uses the cabin pressure to flush the system.
At flight altitudes of approximately 15,000 feet and higher, the pressure external to the aircraft is low enough that the waste-holding tank 12 is evacuated through the evacuation line 14 by the low ambient air pressure external to the aircraft in comparison with the cabin pressure within the aircraft. For altitudes lower than 15,000 feet and while the aircraft is on the ground, evacuation is provided by a vacuum blower 18 located in line with the evacuation line 14. T
edit: Here are the 2 patents, recirc and non-recirc...the patent language gives a very detailed description of the systems and benefits...
Nonrecirculating vacuum flush toilet system utilizing fresh water
RECIRCULATING TOILET SYSTEM