A recording studio is using an external clock as much for synchronization as for anything else, as they often have a situation when devices are daisy-chained together and must work together correctly at every clock beat. The multiple pieces of equipment can't "hear" each other the way an orchestra does, so the master clock is there to make sure all the different pieces are in synch.
It's the daisy chaining effect that CAUSES jitter unless mitigated by the master clock.
On the other hand, with Internet streaming, there's no such synchronization.
PS- Error correction is taken care of by the TCP portion of TCP/IP and handles requests for retransmission when packets are corrupted. Another reason for big buffers, having enough time to ask for a retransmission when an error occurs.