LTE Case:-
Normal Attach procedure is used to register with only EPS network (e.g LTE Only) where as combined attach procedure is used to registered with EPS and Non-EPS networks simultaneously (e.g for both LTE and WCDMA or GSM).
UMTS Case:--
Normal Attach procedure is used to register with only CS Network only where as combined attach procedure is used to registered with CS and PC networks simultaneously.
why we are using this kind of procedure in UMTS is in order to reduce the additional signalling with network.For LTE this is mainly for CS-Fallback purpose.