Below are the passages describing Resurrection Sunday from each of the Gospels.
Matthew 28:1-9: "Now after the Sabbath, toward the dawn of the first day of the week, Mary Magdalene and the other Mary went to see the tomb. And behold, there was a great earthquake, for an angel of the Lord descended from heaven and came and rolled back the stone and sat on it. His appearance was like lightning, and his clothing white as snow. And for fear of him the guards trembled and became like dead men. But the angel said to the women, 'Do not be afraid, for I know that you seek Jesus who was crucified. He is not here, for he has risen, as he said. Come, see the place where he lay. Then go quickly and tell his disciples that he has risen from the dead, and behold, he is going before you to Galilee; there you will see him. See, I have told you.' So they departed quickly from the tomb with fear and great joy, and ran to tell his disciples. And behold, Jesus met them and said, 'Greetings!' And they came up and took hold of his feet and worshiped him. Then Jesus said to them, 'Do not be afraid; go and tell my brothers to go to Galilee, and there they will see me.'"
Mark 16:1-8: "When the Sabbath was past, Mary Magdalene, Mary the mother of James, and Salome bought spices, so that they might go and anoint him. And very early on the first day of the week, when the sun had risen, they went to the tomb. And they were saying to one another, 'Who will roll away the stone for us from the entrance of the tomb?' And looking up, they saw that the stone had been rolled back—it was very large. And entering the tomb, they saw a young man sitting on the right side, dressed in a white robe, and they were alarmed. And he said to them, 'Do not be alarmed. You seek Jesus of Nazareth, who was crucified. He has risen; he is not here. See the place where they laid him. But go, tell his disciples and Peter that he is going before you to Galilee. There you will see him, just as he told you.' And they went out and fled from the tomb, for trembling and astonishment had seized them, and they said nothing to anyone, for they were afraid"
Luke 24:1-7: "But on the first day of the week, at early dawn, they went to the tomb, taking the spices they had prepared. And they found the stone rolled away from the tomb, but when they went in they did not find the body of the Lord Jesus. While they were perplexed about this, behold, two men stood by them in dazzling apparel. And as they were frightened and bowed their faces to the ground, the men said to them, 'Why do you seek the living among the dead? He is not here, but has risen. Remember how he told you, while he was still in Galilee, that the Son of Man must be delivered into the hands of sinful men and be crucified and on the third day rise.'"
But John describes Jesus himself appearing to Mary, following a footrace between John and Peter:
John 20:11-18: "But Mary stood weeping outside the tomb, and as she wept she stooped to look into the tomb. And she saw two angels in white, sitting where the body of Jesus had lain, one at the head and one at the feet. They said to her, “Woman, why are you weeping?” She said to them, “They have taken away my Lord, and I do not know where they have laid him.” Having said this, she turned around and saw Jesus standing, but she did not know that it was Jesus. Jesus said to her, 'Woman, why are you weeping? Whom are you seeking?' Supposing him to be the gardener, she said to him, 'Sir, if you have carried him away, tell me where you have laid him, and I will take him away.' Jesus said to her, “Mary.” She turned and said to him in Aramaic, 'Rabboni!' (which means Teacher). Jesus said to her, 'Do not cling to me, for I have not yet ascended to the Father; but go to my brothers and say to them, "I am ascending to my Father and your Father, to my God and your God."' Mary Magdalene went and announced to the disciples, 'I have seen the Lord'—and that he had said these things to he."
So, to summarize, the Synoptics describe the Resurection as:
Mary Magdalene and possibly His mother visit the grave. They see the stone rolled away, and an angel waiting for them. The angel asks her/them why she/they were looking for "the living among the dead". He then tells them to share the good news.
In John's story:
John and Peter look inside the grave and believe that Jesus was alive, then hide from the Jews in their house. Mary cried outside the grave, but when looking inside sees two angels, who ask her who shes looking for and why she's crying. SHe turns around, and sees who she assumes to be the gardener and ask if he has taken the body. Jesus then opens her eyes and reveals Himself directly to her, causing her to rejoice and then share the good news.
What causes the discrepancy? Did John have a literary reason, did he talk to different witnesses or is there some other reason?