In case of re-direction, target cell does not reserve any radio resources upfront for UE while in case of handover, target cell is prepared for radio resources and then UE is asked to move to target cell. That is the basic difference what I know.
In LTE, if handover is being triggered for an UE eNodeB sends rrc connection reconfiguration to UE with the target cell & configuration details. And in re-direction case, eNodeB triggers rrc connection release to UE with the "redirection with redirected carrier Info"