Lightfoot on Both Hippolytus and Gaius Holding the Same Office of 'Bishop of the Nations' in the Same City in the Same Age

They both flourish during the same pontificates ; they are both styled 'presbyters' and both live in Rome; they both receive only thirteen Epistles as written by St Paul, excluding the Epistle to the Hebrews; they both are men of great learning, though the Roman Church for some generations before and after this time was singularly devoid of literary eminence. And lastly, we have here an explanation of the otherwise not very intelligible statement, that Caius was appointed 'bishop of the Gentiles;' for Hippolytus in the Refutation speaks of himself as holding the episcopal office and addresses the Gentiles more than once as though they were his special charge1. If the designation 'bishop of the Gentiles' is not strictly correct, it was at least a very easy inference from his language in this work it was at least a very easy inference from his language in this work ; and probably he expressed himself similarly elsewhere, when the occasion demanded, as for instance in the treatise on the Universe addressed to the Greeks. [Lightfoot, Gaius or Hippolytus p. 104]

There are simply too many bishops co-existing in the same Roman See.  My guess again is that 'bishop of the nation' was something more than a bishop of a particular city.  I suspect it designated an office like the modern 'Pope.'  Yet more work is needed to sort things all out ...