See any difference there?
You are going to extremes here.
The etymology of the word bishop comes from the Greek word episkopos (åðéóêïðïò), which can be generally translated as bishop, overseer, superintendent, supervisor, or foreman.
The term "Vicar of Christ" is very biblical if you accept Matthew Chapter 16.
By the same token, the Patriarch of Antioch could claim that same title because he too is a Successor of St. Peter.
St. Peter went to Antioch First :)