This is not from a Catholic website, but it clarifies it:
There are several factors at work here. First, I would recommend that you read the Tekton article on inspiration linked to above, so you can understand how small details (the sort which would not qualify as “mistakes” in a way as to undermine the doctrine of inerrancy) wouldn’t concern the Gospel writers or their audience. Then see how the author applies those principles to the Resurrection narratives in his more detailed article The Resurrection Narratives Harmonized Contextually. However, most of the ‘contradictions’ here don’t even fall in that category. They are simply not errors or contradictions at all. Each evangelist is picking and choosing which details to report, so that one evangelist chooses to describe only one angel out of two or leaves out an earthquake. That isn’t a contradiction; it’s the author’s prerogative to choose which details to report as long as an omission does not distort the story. Many biblioskeptics don’t understand logic (see this explanation from Logic and Creation).
Matthew is organizing his material topically in 28:2, not chronologically; the earthquake, rolling away of the stone, and appearance of the angel could have happened at any time before the women got there. A translation of the Greek which properly brings this out would be “And behold there had been a great earthquake, for the angel of the Lord descended from heaven and went and rolled away the stone and sat on it.” We do things like this in writing even today, so it’s not a contradiction in chronology.
The question about how many angels there were, one or two, is another selection issue. Matthew and Mark choose to depict the one who did the most talking, Luke added the detail that there was another there too. The same goes for how many women saw Jesus. It’s not surprising that Mary Magdalene is highlighted in the accounts, because she was Jesus’ most prominent female follower, and there’s evidence that she was actually funding His (and His disciples’) ministry.
Carson’s commentary on John’s gospel has the best discussion I’ve found on the alleged Resurrection account discrepancies.1 To sum it up, some of the discrepancies are on the trivial level and are based on the selectivity of the Gospel writers in choosing some details and leaving out others. Critics who say these things are actual contradictions are imposing their ridiculously rigid, uniquely Western, views on what consists of precise reporting. No one in ancient Palestine would take things like who went to the tomb to be a contradiction. Other things are judged to be contradictions based on too little evidence. Carson’s harmonization is worth quoting at length:
“For example, Mary Magdalene finds the tomb empty and, upon hearing her report Peter and the beloved disciple rush off to the tomb. Eventually they return to their own homes (v. 10), while Mary is found outside the tomb crying (v. 11). When or how did Mary get there? For almost two thousand years it has been assumed, not unreasonably, that she returned to the garden alone, or possibly in the wake of the two running men. Must a narrator report each mechanical step? This lack of information, coupled with modern assumptions about the way ancient editors and communities constantly cut up their sources and patched them together in new pieces, has led to several ingenious but unbelievable reconstructions.”("http://creation.mobi/claimed-bible-errors#endRef2")
Constructing a chronology for the Resurrection appearances is one of the more complicated issues; this is because we’re not exactly sure how the different authors’ accounts relate to the details in the other authors’ appearances. This is because there is nothing that would force the disciples to record the resurrection appearances in precise chronological order;
“in terms of the fundamental meaning and significance of each resurrection account, and in terms of the way they were first preached, each of Jesus’ resurrection appearances could stand more or less alone: the entire sequence of appearances was not necessary to establish meaning and credibility. This means that the student of the Gospels must proceed with extraordinary caution when historical or source-critical harmonizations are attempted.”("http://creation.mobi/claimed-bible-errors#endRef3")
Modern news stories covering the same event have much the same sort of ‘contradictions’ skeptics point to in the Gospel accounts
JP Holding’s article on harmonization points out that modern news stories covering the same event have much the same sort of ‘contradictions’ skeptics point to in the Gospel accounts, while at the same time not having any “mistakes” in the sense of false elements to the report. The Christian Thinktank also has a very good article; especially the point about the apparent discrepancies lending credibility to the Gospels as four separate witnesses to the Resurrection; absolute agreement in every small detail would be evidence that they had depended on each other to such an extent that they could not be considered independent witnesses.