The advanced algorithm used by the PowerVR is partly based on search the intersecting line of 2 planes. To do real time shadows you let infinite planes tart from you light source and you let the go around the object casting its shadow. The intersecting lines between the surrounding objects (surfaces) and the planes coming from the light source will determine the Real shadow casted by that object. Light Volumes are similar but instead of casting a shadow you do an inversion and you are casting light.

The other chipsets are incapable of doing hardware shadows and have to use a software equivalent, this means that it will be slower and much less realistic. Usually those software shadows are static and do not move with the light source, they always fall straight under the object. Recreating the same realism as with the powerVR is possible but would require too much time of the main processor to be used.