Many contend that Judas the son of Ezekias (Hezekiah) who led the uprising centered in Sepphoris around the time of the death of Herod the Great (Jewish Antiquities 17:271-272) and Judas the Galilean, who led the resistance to the census under Quirinius (JA 18:4f) were the same person. The claim seems to rest primarily on the fact that they had the same name, ignoring how common the name Judas (Judah) was among Jews (Judeans) at that time. The first argument against this claim is that Josephus does not link the two. The second Judas is identified by his city of origin, Gamala, and not by any famous father. The former Judas has royal aspirations. The latter Judas considers paying tribute to Rome a form of slavery and contend that God is their only Ruler and Lord (JA 18: 23). This position is hardly amenable to one who himself wants to be king. It is more favorable to the arrangement during much of the Hasmonean era when the High Priest governed and there was no king, an arrangement that Josephus himself favors.
Identifying the two Judases is convenient, but unsupported.
Why does this matter? Those who saw Jesus as the messiah seem to be more in the tradition of the son of Ezekias. This could be a sentiment especially prominent in the backwaters of Galilee. Josephus links Judas the Galilean, whose uprising was not in Galilee but in Jerusalem, with a group of Pharisees, with what he calls the Fourth Philosophy, and eventually with the Zealot Party of the rebellion of 66 CE. To me the Fourth Philosophy does not resemble the Jesus movement, cf. JA 18:23-25.