Julius and Augustus you mean, both were Caesars (Augustus, AKA Octavian, was adopted).
History is not my field, I am probably making multiple mistakes and oversimplifying, but I don't see something in that link that disproves what I said. Today, we often refer to Augustus as Augustus Caesar or Caesar Augustus (less frequently, Emperor Augustus). I also think it's interesting to point out Julius's first name in light of the previous discussion, as that's where the month name comes from.