That is correct, MUQ.<quoted text>
I understand what you mean. The "poor Matthew", he had to compare Jesus with Moses and find "parallels between them" while there are no two personalities who are so different from each other as Moses and Jesus"!!
But I think you already know that Gospel of Matthews we have in our hands today was not written by Matthew , One of the Chosen Twelve Disciple of Jesus.
It is an anonymous book on which some "unknown hand" has put on title page "Gospel according to Matthew".
No one knows exactly, who wrote these gospels. Even Bishops agree that John was written by many Johns.
Luke and Matthew copied Mark wholesale. The Church realized this very late and John was ordered.
Yes, that is why they are called, "Gospel, according to.....".