The terminology is not consistent. Any serve with a heavy topspin component is considered a kick serve by many. In my mind, kick serves come in 2 basic flavors, a topspin kick and a twist kick. Both have a component of slice (sidespin) but the latter has a much stronger spiral spin component. The extra spiral spin accounts for the greater side bounce. (Note that this is not caused by regular side spin). The 2 flavors are really part of a continuum of kick serves.
.