How was Jesus characterized differently in each of the four gospels (Mark, John, Matthew, Luke)? Did each of the four gospels characterize him differently?
Yes each gospel characterized him differently partly because of the individual characteristics of the authors and the audience their gospel was directed towards.
The gospel of Matthew was written to a Jewish audience, There is evidence that the original gospel of Matthew was written in Hebrew or aramaic, possibly around AD 50. This original Hebrew version was likely used by the later writers Mark and Luke. Matthew characterizes Jesus as the Messiah the anointed one. Jesus is seen as the descendent of King David and a King in his own right
The gospel of Mark was written to a Roman audience. This gospel was probably written before AD 59 and definitely before the sack of Jerusalem in AD 72. Tradition relates that Mark wrote the account from verbal instructions from the apostle Peter. Mark frequently describes Jesus as the Son of Man. Jesus is portrayed as a man of action, doing miracles, and challenging the authority of Jewish authorities. ( who were in rebellion against Rome)
The gospel of Luke was written by a Greek, to a Greek audience. It is explicitly addressed to the most excellent Theophilus apparently a Greek of high social status. As the book of Acts the companion book to the Gospel ends before the death of Paul it had to been written before the execution of the apostle Paul by Nero in about AD 52. Luke calls Jesus the Son of the Most High. The Greeks believed in demigods descended from the Gods of Olympus. Luke portrays Jesus as superior to any man or demigod in Greek literature.
The gospel of John was probably written about 90 AD. It was written to a Christian audience that had already believed in Christ.
The church was under attack by alternative views of Christ by the agnostics. John takes great pains to counter the agnostic view of Christ, that he was not truly human but a spirit that occupied a human body, and imparted secret knowledge to a select few. Jesus is shown to be truly both man and God, who imparts knowledge of himself freely to all in the gospel of John