I pointed this out on a post a while back. Before we go to the differences, let’s point out the similarities first.
All four gospels (Matthew-Mark-Luke and John) agree about Mary Magdalene being present at the empty tomb. In fact, John himself seems to imply the existence of others with her - as in the synoptics - because Mary Magdalene says ‘we (not ‘I’) do not know where they have laid him.’
Now on the first day of the week Mary Magdalene came to the tomb early, while it was still dark, and saw that the stone had been taken away from the tomb. So she ran and went to Simon Peter and the other disciple, the one whom Jesus loved, and said to them, “They have taken the Lord out of the tomb, and we do not know where they have laid him.”
In fact, disregarding the differences in detail (which women went to the tomb? How many angels?) both traditions - the synoptic and Johannine - agree in three core, basic elements.
(1) (Female) disciples went to the tomb of Jesus early Sunday morning.
(2) One of these was Mary Magdalene.
(3) The tomb was found empty - the body of Jesus was nowhere to be found.
As for the other women besides Mary Magdalene, we have the following:
Mark: Mary Magdalene, Mary the mother of James (likely the “Mary the mother of James the younger and Joses” / “Mary the mother of Joses” mentioned in 15:40, 47), Salome
Matthew: Mary Magdalene, the other Mary (cf. 27:61 - perhaps the “Mary the mother of James and Joseph” mentioned in 27:56?)
Luke: Mary Magdalene, Mary the mother of James, Joanna, “the other women with them”
At best, you might accuse the gospels of adding more women, but as they are, there’s no contradiction as to who went - in the sense that “this other Mary did
not go, it was actually someone else.” At least all three synoptics agree in two out of three names: Mary Magdalene, plus another Mary, the mother of James and Joses/Joseph.
The only real difference is Mark’s Salome and Luke’s Joanna, but then again, without having to posit (as some people did) that Salome and Joanna are really one and the same person, one may argue that Salome is covered by Luke’s rather general “the other women with them.”
I think you’re confusing ‘authorship’ with ‘inspiration’.