If network supports extended service request for packet switch then UE sends Extended Service Request (packet services via S1) in response to PS paging. If network does not support ESRPS feature then UE sends Service Request in response to PS paging.
In essence, UE initiates either service request or extended service request for the PS paging depends on the network supported feature i.e . ESRPS.
This is what I know. I am looking forward to others to respond.