Redirection :Its a connected mode procedure and this decision is entirely left to the NW. So what happens the NW will send RRC Connection Release Information with some RedirectCarrier Information like : TargetRATType , Frequency/EARFCN/UARFCN/ARFCN. And Based on that information UE can be redirect to the same RAT or Different RAT.
Handover: It is also a connected mode procedure and initiated by Network. Network will ask UE to send the Measurement reports of the serving cell or the Target Cell and based on that NW will initiate Handover.