The main difference is that the Phone Bridge operates inside of Zoho ONLY and the normal integration is through the Callinize Chrome Extension.
The Chrome Extension offers features such as follow-up task creation, caller/callee history, and user notifications. Most importantly, you will see a popup for every call on EVERY Chrome tab. This means you will see a notification even if you are not in Zoho at the time.
In ZOHO, the Phone Bridge logs calls as notes under a single API user, while the normal integration logs calls as completed activities as user who created it.