What is the difference between B2BUA and proxy in SIP protocol?

A B2BUA (Back 2 Back User Agent) acts as a server on one end and a client on the other to handle all aspects of a VoIP Call, including session initiation and session disconnect. This will allow you to add features such as billing, hiding network complexity and addresses, etc. Asterisk is a type of B2BUA. A proxy, on the other hand, handles the hand off to wide areas from devices on the local side, for instance, but may allow the intermediate devices to handle the call complexity including session set up and disconnect.