What is the difference between Baptism of Jesus and Baptism of others?

From a Protestant, Evangelical perspective, the baptism of Jesus by the prophet John was not a baptism of repentance; rather, it was a baptism into a way of life for Jesus which culminated in his ultimate baptism: his cross-death for the sins of the world.

Recall that Jesus asked James and John, the sons of Zebedee, a poignant question when they asked if they could sit next to Jesus when he came into his kingdom. For reasons of context, I include a lengthy passage:

Jesus Predicts His Death a Third Time

32 They were on their way up to Jerusalem, with Jesus leading the way, and the disciples were astonished, while those who followed were afraid. Again he took the Twelve aside and told them what was going to happen to him. 33 “We are going up to Jerusalem,” he said, “and the Son of Man will be delivered over to the chief priests and the teachers of the law. They will condemn him to death and will hand him over to the Gentiles, 34 who will mock him and spit on him, flog him and kill him. Three days later he will rise.” The Request of James and John 35 Then James and John, the sons of Zebedee, came to him. “Teacher,” they said, “we want you to do for us whatever we ask.” 36 “What do you want me to do for you?” he asked. 37 They replied, “Let one of us sit at your right and the other at your left in your glory.” 38 “You don’t know what you are asking,” Jesus said. “Can you drink the cup I drink or be baptized with the baptism I am baptized with?” 39 “We can,” they answered. Jesus said to them, “You will drink the cup I drink and be baptized with the baptism I am baptized with, 40 but to sit at my right or left is not for me to grant. These places belong to those for whom they have been prepared.” 41 When the ten heard about this, they became indignant with James and John. 42 Jesus called them together and said, “You know that those who are regarded as rulers of the Gentiles lord it over them, and their high officials exercise authority over them. 43 Not so with you. Instead, whoever wants to become great among you must be your servant, 44 and whoever wants to be first must be slave of all. 45 For even the Son of Man did not come to be served, but to serve, and to give his life as a ransom for many" (Mark 10:32-45 NIV, my emphases).

Truly, Jesus lived in the shadow of the cross. Several times (or more) Jesus predicted his death to his disciples, but each time they failed to grasp what Jesus meant (see, for example, Mark 9:30-32 NIV). Only after his resurrection did the pieces of the puzzle come together for them.

Peter in particular actually rebuked Jesus for his plain teaching about his coming trial, death, and resurrection. Jesus in turn rebuked Peter, saying,

“Get behind me, Satan! For you are not on the side of God, but of men” (see Mark 8:31-33 RSV).

We read that after he was baptized by John,

Jesus, full of the Holy Spirit, returned from the Jordan [River] and was led around by the Spirit in the wilderness for forty days being tempted by the devil (Luke 4:1-2 NASB).

With the exception of Jesus' transfiguration (and his death, burial, and resurrection), his baptism was perhaps the most pivotal event in his adult life. The baptism signaled not only the beginning of his public ministry, but it foreshadowed the giving of his life at Calvary as a ransom for many.

In conclusion, as for Jesus' baptism being a fulfillment of all righteousness, that fulfillment was also, perhaps, the capstone of having successfully completed 30 years of humble obedience to the Father. You'll recall that at Jesus' baptism,

. . . the Holy Spirit descended upon Him in bodily form like a dove, and a voice came out of heaven, "You are My beloved Son, in You I am well-pleased" (Luke 3:22 NASB).

With that declaration by the Father, Jesus did battle with the devil and thereafter began in earnest his journey to Calvary.