Hi peacefulpete, I have done some more research regarding the two references to Jesus Christ in the extant writings of Josephus. I have read multiple conflicting arguments (when I include comments by Richard Carrier on this matter) about the longer passage and thus I am not sure if the entire passage (not just portions of it) were interpolated into it by Christians, but I am still inclined to believe that most of it is authentic. If most of it is authentic, then it would provide the context for the identify of the particular Jesus who is "called Christ" who is mentioned in the shorter passage, which is the later passage. However, I am very confident that the shorter passage is not an interpolation, and that it refers to Jesus Christ of Christianity. To me the article at https://www.history.com/news/was-jesus-real-historical-evidence makes a strong case for the shorter passage being about the Christian Jesus Christ. To me the article at https://strangenotions.com/an-atheist-historian-examines-the-evidence-for-jesus-part-2-of-2/ (which is written by an atheist) makes even a stronger, and very convincing, argument that is about the Christian Jesus Christ. For Carrier's views, primarily about the longer passage, (which to me some are stated in a very contorted and convoluted way), I have read https://www.richardcarrier.info/archives/12071 , https://www.richardcarrier.info/archives/7437 , and https://www.richardcarrier.info/archives/4391 .
The https://strangenotions.com/an-atheist-historian-examines-the-evidence-for-jesus-part-2-of-2/ article is written by an atheist who says the following about himself. "Tim O'Neill is an atheist blogger who specializes in reviews of books on ancient and medieval history as well as atheism and historiography. He holds a Master of Arts in Medieval Literature from the University of Tasmania and is a subscribing member of the Australian Atheist Foundation and the Australian Skeptics." His article says in part the following.
'Ananus executed some Jews without Roman permission and, when this was brought to the attention of the Romans, Ananus was deposed. This deposition would have been memorable for the young Josephus, who had just returned from an embassy to Rome on the behalf of the Jerusalem priests. But what makes this passage relevant is what Josephus mentions, in passing, as the cause of the political upheaval:
"Festus was now dead, and Albinus was but upon the road; so (the High Priest) assembled the Sanhedrin of judges, and brought before them the brother of Jesus, who was called Messiah, whose name was James, and some others; and when he had formed an accusation against them as breakers of the law, he delivered them to be stoned."
This mention is peripheral to the story Josephus is telling, but since we know from Christian sources that Jesus' brother James led the Jesus sect in Jerusalem in this period, and we have a separate, non-dependent, Christian account of James' execution by the Jerusalem priesthood, it is fairly clear which "Jesus who was called Messiah" Josephus is referring to here.
Almost without exception, modern scholars consider this passage genuine and an undisputed reference to Jesus as a historical figure by someone who was a contemporary of his brother and who knew of the execution of that brother first hand. This rather unequivocal reference to a historical Jesus leaves Jesus Mythicists with a thorny problem, which they generally try to solve one of two ways. They either claim:
(i) "The words "who was called Messiah" are a later Christian interpolation"
Since it is wholly unlikely that a Christian interpolator invented the whole story of the deposition of the High Priest just to slip in this passing reference to Jesus, Mythicists try to argue that the key words which identify which Jesus is being spoken of are interpolated. Unfortunately this argument does not work. This is because the passage is discussed no less than three times in mid-third century works by the Christian apologist Origen and he directly quotes the relevant section with the words "Jesus who was called the Messiah" all three times: in Contra Celsum I.4, in Contra Celsum II:13 and in Commentarium in evangelium Matthaei X.17. Each time he uses precisely the phrase we find in Josephus: αδελφος Ιησου του λεγομενου Χριστου ("the brother of that Jesus who was called Messiah"). This is significant because Origen was writing a whole generation before Christianity was in any kind of position to be tampering with texts of Josephus. If this phrase was in the passage in Origen's time, then it was clearly original to Josephus.
(ii) "The Jesus being referred to here was not the Jesus of Christianity, but the 'Jesus, son of Dameus' mentioned later in the same passage."
After detailing the deposition of the High Priest Ananus, Josephus mentions that he was succeeded as High Priest by a certain "Jesus, son of Damneus". So Mythicists try to argue that this was the Jesus that Josephus was talking about earlier, since Jesus was a very common name. It certainly was, but we know how Josephus was careful to differentiate between different people with the same common first name. So it makes more sense that he calls one "Jesus who was called Messiah" and the other "Jesus son of Damneus" to do precisely this. Nowhere else does he call the same person two different things in the same passage, as the Mythicist argument requires. And he certainly would not do so without making it clear that the Jesus who was made High Priest was the same he had mentioned earlier, which he does not do.
The idea that the Jesus referred to as the brother of James was the later mentioned "Jesus son of Damneus" is further undercut by the narrative in the rest of Book XX. In it the former high priest Ananus continues to play politics and curries favour with the Roman procurator Albinus and the new high priest by giving them rich presents. This makes no sense if Jesus the brother of the executed James was also "Jesus the son of Damneus", since the new high priest in question is the same Jesus ben Damneus - the idea that he would become friends with his brother's killer just because he was given some nice gifts is ridiculous.
Mythicists are also still stuck with the phrase "who was called Messiah", which Origen's mentions show can't be dismissed as an interpolation. They usually attempt to argue that, as a High Priest, Jesus the son of Damenus would have been "called Messiah" because "Messiah" means 'anointed" and priests were anointed with oil at their elevation. Since there are no actual examples of any priests being referred to this way, this is another ad hoc argument designed merely to get the Mythicist argument off the hook.
So the consensus of scholars, Christian and non-Christian, is that the Antiquities XVIII.3.4 passage is authentic despite some obvious later additions and the Antiquities XX.9.1 passage is wholly authentic. These references alone give us about as much evidence for the existence of a historical "Jesus, who was called Messiah" as we have for comparable Jewish preachers and prophets and is actually sufficient to confirm his existence with reference to any gospel or Christian source.'
Also please read what that same article says about what Tacitus wrote about Jesus and how that is also strong evidence that Jesus (the one who was and is called Christ) was a historical person. The conclusion in the article mentions in part the following.
"The original question we concerned ourselves with was whether historians regard the existence of Jesus to be "historical fact". The answer is that they do as much as any scholar can do so for the existence of an obscure peasant preacher in the ancient world. There is as much, if not slightly more, evidence for the existence of Yeshua ben Yusef as there is for other comparable Jewish preachers, prophets, and Messianic claimants, even without looking at the gospel material. Additionally, that material contains elements which only make sense if their stories are about a historical figure.
The arguments of the Jesus Mythicists, on the other hand, require contortions and suppositions that simply do not stand up to Occam's Razor and continually rest on positions that are not accepted by the majority of even non-Christian and Jewish scholars."