There are several different styles of "swing hangers" regarding is the upper pin is above or below the transom of the truck frame. It boils down to what was the manufactures patent and the railroads preference.
As far as the motion and how the system works, the equalizers and the coil springs make up the vertical suspension which adjusts for most of the ilreagularities of the track. The truck frame is supported by the equalizers. The body is hanging from the truck frame through the swing hangers to provide the laterial motion of the truck. In a properly set up truck the swing hangers are canted outward so the distance between the lower pins supporting the spring plank is wider than the upper pins attached to the transom. This produces a natural (gravity powered) centering effect that also dampens the swinging motion while the car is in motion.
The longer swing hangers produce a smoother ride akin to longer a truck wheel base.
Modern trucks (1940's and 50's) moved the swing hangers outside the truck frame for a wider stance, bolster anchors were added to replace the chafing irons between the truck bolster and transoms, and the elliptical springs were replaced with coils with snubbers or shock absorbers to reduce ossilations.
The new trucks under the SUperliner II, horizon and veiwliners are a completely different animal. My understanding is that they have eliminated the swing type suspension and moved the centerplate down onto the truck frame. The coil springs that were between the truck bolster and spring plank moved over the body bolster to further control roll and stability at higher speeds.
Sorry about any spelling or typos, as this counts as a five minute babble blast responce.
Paul