One basic difference is "In handover procedure, target cell would be prepared and UE will latch on target cell based on the configuration sent by source enodeb to UE. Whereas in re-direction, target cell would n't be prepared for the Ue , And UE leave current cell and will try to latch on the cell/frequency, communicated by source eNB to UE.
So during handover procedure, UE will continue with the services which were being used by UE. But in case of re-direction, services will be interrupted.