When Jesus appointed the disciples he actually chose two people called James: "These are the twelve he appointed: Simon…James son of Zebedee and his brother John…Andrew, Philip, Bartholomew, Matthew, Thomas, James son of Alphaeus, Thaddaeus, Simon the Zealot and Judas Iscariot…" Mark 3:16-19
So there was James, the brother of John son of Zebedee and James, the son of Alphaeus. (There is also a third person named James mentioned in the New Testament, he was the brother of Jesus and author of the book named James.)
We are not told anything about the second disciple named James, except he was the son of Alphaeus. In Mark 2:14 we discover that Matthew, the tax collector, is also the son of Alphaeus. It is likely that James and Matthew were related. However they are never mentioned together, perhaps because they were diametrically opposed to each other.
Bible historians believe that this second disciple called James, like Simon, was a Zealot. Zealots were a political group who believed the best way to be free of Roman oppression was through armed revolt. Zealots hated the very presence of Romans in their land and hated those who cooperated with them…like tax collectors. Not only did Jesus have Zealots and tax collectors as disciples but also a couple of fishermen in need of anger management (Luke 9:54) and one who spoke even when he didn't know what to say (Mark 9:6)! The group Jesus chose had every reason to disintegrate into factions.
Yet Jesus managed to galvanize this group by focusing on the one thing they had in common. They all wanted to see God's kingdom come and were prepared to put aside their prejudices and agendas in order for that to happen.
God continues to choose people as leaders who do not naturally work well together. The challenge for us as God's people is to put aside our prejudices and agendas for the bigger purpose of growing God's kingdom.