Yes, "stories" plural.
When thinking about Christmas as the traditional celebration of the birth of Jesus (and not a marketing ploy), Christians should remember that two of the four gospels make no mention whatsoever of the birth of Jesus, and the other two gospels tell stories that are not just different, but actually conflicting.
A traditional Christmas celebration will include readings from both Luke and Matthew, and mix them together, but let's take a look at what the Bible actually says.
In the book of Luke, Mary and Joseph start in the town of Nazareth, but then must go to the town of Bethlehem in order to comply with a census supposedly ordered by Caesar Augustus (for which there is no historical evidence whatsoever). There is no room at the inn so Mary gives birth to Jesus in the stable. Shepherds are told of the birth of Jesus by angels and they come to the stable to see the baby Jesus. Mary and Joseph travel to Jerusalem with Jesus, and then eventually return to Nazareth. No mention of any wise men from the east, no star over Bethlehem, no slaughter of male babies, and no trip to Egypt.
In the book of Matthew, the story is quite different. Mary and Joseph seem to be living in Bethelem already (i.e., no census by Caesar Augustus) and Jesus is born in their home. No mention of any stable, manger, or shepherds. Instead, wise men come from the east, follow a rising star to Bethlehem, and offer gifts to Jesus. Then Mary, Joseph, and Jesus flee to Egypt when Herod orders the death of all children in or around Bethlehem that are two years of age or younger, another seemingly noteworthy event for which there is no other historical evidence. After Herod dies, Mary and Joseph return to Israel, but are still afraid to return to Bethlehem in Judea, and instead settle in Nazareth in Galilea, where they have apparently never lived before.
It is also remarkable that the gospels of Luke and Matthew tell these stories once and then never mention them again. Jesus himself never refers to his own birth, and he is never asked about it, which seems strange given the unusual (to say the least) circumstances of his birth. And there is no mention of the birth of Jesus in the book of Acts, any of the letters of Paul, or any other part of the New Testament.
Finally, we have to confront the fact that the authors of both Luke and Matthew wanted Jesus to be born in Bethlehem in order to fulfill a prophecy, but that he should be "from" Nazareth in order to fulfill another prophesy. So it appears that each of the authors constructed a story to explain why Jesus was born in Bethlehem, and they constructed different stories. The authors also had very different goals for their stories, because Matthew describes Jesus as royalty, descended from King David, sought after by wise men from the east, and seen as a threat by King Herod, while Luke describes a lowly birth in a stable noticed only by angels and shepherds.
What are we to make of all this? Two conclusions seem unavoidable.
The first conclusion is that the stories of the birth of Jesus in Matthew and Luke cannot be considered factual. They contradict each other, so they can't both be accurate, and there are too many problems with them to believe that either is historically accurate.
The second conclusion is that the stories of the birth of Jesus are not very important to Christianity as a faith, and so whether you want to believe or disbelieve the stories is also not very important. You can be a "good Christian" (whatever that might mean) whether you choose to believe the story in Luke, or the story in Matthew, both of them, or neither of them.
The corollary to these conclusions is that, once we have stripped the stories of any historical or theological significance, we can have fun with them. We can transform the wise men of the Bible into three kings, and we can make up names for them, such as Caspar, Melchior, and Balthasar. We can construct scenes in which the three kings from Matthew are mixed in with the shepherds and manger from Luke. We can write songs about lame shepherds (Amahl) and little drummer boys.
All good fun. And isn't that what Christmas is all about?