Both are (GTP-C) tunnel management messages.
Modify bearer request *is initiated by MME/S4-SGSN and/or from S-GW to P-GW*
- Here you are not adding or deleting any resources/bearers.
- This message is used when there is no change on allocated bearers, Only the cause is user is moving from one place to another. Basically Radio Part is changing. This information MME should inform to all Core Network Elements (S-GW) and it helps them to attain the resources and handovers case too. It will just modify the bearers.
- After getting the response of Modify Bearer Request it indicates that User Plane is ready to carry the user data as Control plane is done and now data can flow in between E-UTRAN and S-GW.
Update Bearer Request: *is initiated by P-GW to S-GW and/or from S-GW to MME/S4-SGSN*
I want to explain here with example. Suppose you are playing a online game in your Mobile. It requires a promised speed to avoid the delay and you are subscribed for that too. Now suddenly you got to know that you have to send a mail to your boss but you don't want to close your game. For this purpose you need more resources. Here Update Procedure will come.
You already have dedicated bearers with you. Your packet forwarding is happening through P-GW but you need more resources. In this case P-GW will initiate the message Update Bearer Request.