One event or two?
The timing of the event/s is complicated by the fact that Matthew and Mark place it after the arrest of John the Baptist, while Luke does not mention John's arrest hereimprisonment until chapter 7. On the other hand Matthew and Mark place itthe event immediately after Jesus' temptation in the wilderness, while Luke first recounts stories of Jesus earliest ministry in Capernaum, including a visit to Simon Peter's home, the first mention of Peter in Luke's Gospel.
WeBut we do not need to resolve the question of whether this was one event or two, in order to understand the most important difference in the two accounts. Matthew and Mark use it to emphasize the faith of the disciples to "leave their nets" and follow Jesus. (Matthew 4:20) Luke uses it as an analogy to witnessing: by casting their nets deeper they receive a greater harvest.
Luke's key point: the Message is Universal
This reflects Luke's attitude that the Christian mission must not be limited to the shallow areas near the shore (close to home), as compared to Matthew's report that Jesus sent his disciples only to the "lost sheep of the house of Israel." (Matthew 10:6) By casting their nets deeper, the disciples not only get more fish but many differentmore varieties, symbolizing the universality of the Christian message.
Thus, whether it was the same event or not, we can understand that Mark and Matthew's account emphasizes the idea of leaving behind one's former life to follow Christ, while Luke's emphasizes the theme of casting a deep symbolic net, farther into the sea, in order to bring the win the greatest number and variety of people to God.