There are four complete lists of the twelve apostles in the New Testament (I am including the Acts list which does not list Judas Iscariot though he is mentioned in the chapter). They are found in Matthew 10:2-4, Mark 3:16-19, Luke 6:13-16 and Acts 1:13. Ten of the twelve apostles are the same in all four lists. Two of the lists name Simon the Canaanite and two mention Simon Zelotes. Certainly, this is one and the same person. That leaves Thaddaeus in Matthew and Mark and Judas the brother of James in Luke and Acts. By elimination they must be one and the same.
The only other logical possibility would be that these are indeed two men and one replaced the other during the ministry of Christ. However, this is not possible because of a couple of things. First, there is no hint of any such switch. But second (and conclusive) is the fact that Mark 3:13- 9 and Luke 6:12-16 are parallel passages recording the same event. In both, Jesus went up to a mountain and then returned. In both, He ordained twelve men to be His apostles. This could only refer to one event and time. In Mark, one on the list is Thaddaeus. In Luke, the parallel name on the list is Judas the brother of James. They must be one and the same.