Naw, it's not close to a vane pump.
http://www.roymech.co.uk/Related/Pumps/ ... ement.html
The cool thing about a swashplate pump is that you can vary the engle of the swashplate while it's working, and thus vary the volume pumped. The trouble with a swashplate pump is that it's expensive. It requires precision machining, and it's a bit complicated to assemble and maintain.
Most pumps I know of vary their pressure and volume based on RPM. Of course, with a swashplate it too will pump relative to RPM. But just by varying the swashplate angle, which is very easy to do during operation, you can control the volume pumped. Things like a vane or positive displacement rotor pump require a reservoir and check valves to control pressures and volumes. And of course, noo matter what the demand from the hydraulic system, the pump is always trying to pump fluid when it's turning. A lot of energy is thrown away when a check valve opens to relieve pressure or drain back to the reservoir. But with a swashplate, you need more volume and/or pressure, just move the swashplate angle. Less, same rule aplies.