Prompted by a nifty Venn diagram I saw on Twitter, I thought about composing a Venn diagram to illustrate this post. But they turn out to be a bit time consuming to draw and to type text into, so I will stick to text only!
So, here's a thing about the canonical gospels, they are very interesting on the origin of Jesus Christ.
Mark simply introduces Jesus as a fully adult person.
Matthew begins with a genealogy (which (likely) later Luke will only partially replicate when he gives his own genealogy) and that genealogy goes all the way back to Abraham.
Luke begins with the story of the conception of John the Baptist, as a preluded to the story of the conception of Jesus. Only later, chapter 3, does his genealogy appear, and that goes all the way back to Adam.
The origin of Jesus is pushed even further back in John's Gospel, to the time before time (1:1-3). John shows no interest in telling the story of Jesus birth as an historical, personal, familial stort. Nevertheless, John shows great interest in the theology of the birth: the Word became flesh (1:14).
So, noting these major differences across the four accounts, we are left with observations about the minor differences and similarities between Matthew and Luke's accounts of the birth of Jesus.
One way to set down our observations, prompted by the Venn diagram I saw, is this:
What do Matthew, Luke and the cultural Christmas of the West have in common?
Jesus, Mary, Joseph, Bethlehem
What do Matthew and the cultural Christmas of the West have in common?
Sages from the East, a guiding star, gifts.
What do Luke and the cultural Christmas of the West have in common?
Inn [not actually an inn, but a lodging, possibly with relative], stable [not actually mentioned in Luke], manger, shepherds from nearby fields, angels.
What does the cultural Christmas of the West have which Luke does not have?
Innkeeper [so, update, add here "inn" and "stable"]
What do John and the cultural Christmas of the West have in common?
Nothing. Not even the innkeeper :)
What do Matthew and Luke have in common?
Jesus, Mary as his mother who conceives him through the power of God and not through male sperm, Joseph as her husband or husband to be but is not Jesus' biological father, Bethlehem as place of birth, Nazareth as place of upbringing.
What are key differences between Matthew and Luke?
Matthew locates the birth historically in the reign of King Herod over Palestine (a province of Rome).
Luke locates the birth historically in the reign of Caesar Augustus over the whole Roman empire.
Perspective and divine communication
Matthew tells the story from Joseph's point of view, and God communicates with Joseph through dreams.
Luke tells the story from Mary's point of view, and God communicates with Mary (and other figures in the story) through angels.
Matthew tells us that the chief act of visitation of the newborn baby is a group of Eastern sages who are guided astrologically to the birthplace. Symbolically, this group represent the world beyond the Jews, an expanded world which Jesus has come to save.
Luke tells us that the chief act of visitation of the newborn baby is a group of shepherds, from nearby, aroused from slumber and alerted to the birth by an angelic choir. Symbolically, this group represents the harmony and normality of the world Jesus enters. While Jesus will disrupt the world somewhat, essentially his coming as "Saviour, Messiah and Lord" (2:11) is not a threat to the peace of the Roman empire (and nor is the movement he inspires).
Matthew has no account of Jesus being presented in the Temple in Jerusalem as a baby, or making a pilgrimage there as a near pubescent boy.
Luke accounts for both visits (2:22-51).
Geography: resolution of a conundrum
Matthew and Luke agree on two geographical facts of Jesus' life: he is born in Bethlehem, he grows up in Nazareth. How to account for being in one place and then in another?
Matthew explains the relationship of Nazareth to Bethlehem in terms of a need to flee to Egypt, and, on return to Palestine, a need to be in a different town to Bethlehem, so Nazareth is where the Holy Family settles.
Luke explains the relationship of Nazareth to Bethlehem in terms of Nazareth as home to Joseph and Mary but a journey to Bethlehem is required by virtue of a census. There is no need to flee Herod's troops in Luke's telling so, instead of Matthew's urgent escape to Egypt, the Holy Family return in quietness to Nazareth.
Now there are many intriguing things here in this verbalised Venn diagram of overlaps and differences, and I am not going to cover them all!
One is that, when New Testament scholars talk abou a document called Q (short for Quelle, or "source"), they refer to a hypothetical document which included all the common material between Matthew and Luke which is not also found in Mark's Gospel; except, if you look up what scholars propose as the contents of Q, you will rarely, if ever, find the Lukan-Matthean common elements in the birth story of Jesus listed or cited.
There is no Christmas in Q but there ought to be.
Another intriguing element is whether Luke knew Matthew or Matthew knew Luke or each is independent of one another.
In favout of independence are the significant variations in the stories each tells. It certainly looks like, with both knowing bare facts such as Mary, Joseph, Mary a virgin, birth in Bethlehem, upbringing in Nazareth, each tells a story of the birth of Jesus and immediate and subsequent events independently of each other. One would have to favour the hypothesis of independence.
Yet, and yet ... (here only discussing the possibility of Luke knowing Matthew's Gospel), is it possible that the differences arise precisely because Luke both knows Matthew and for apologetic and theological reasons wants to tell the story differently?
Consider, for example, the "coincidence" that Matthew and Luke both have a significant visitation to the baby. Sages are different to shepherds but both turn up prompted by communication from beyond themselves. There are theological reasons (alluded to above) for one telling of sages and the other of shepherds.
Consider also the "coincidence" that both Matthew and Luke have to work hard to explain the discrepancy between Bethlehem as the place of birth and Nazareth as the place of upbringing. Matthew gets the Holy Family from Bethlehem to Nazareth both plausibly (to avoid Herodian danger that won't go away) and circuitously (via Egypt, but in accordance with prophecy).
If Luke knows Matthew, and does not want to bother with the Herodian threats to Jesus' in his early life, then his story tackles the geographical discrepancy from a reverse perspective. Joseph and Mary are residents of Nazareth so there is a need to explain how they ended up in Bethlehem for the birth of Jesus.
So Luke tells of a census and its requirements for Joseph to register in Bethlehem - but look up any decent sized commentary on the early verses of Luke 2 and you will see considerable stretching and straining to align what Luke says (e.g. about Quirinius) with what we think we know about censuses and Syrian governors and registration requirements around the 4 BC (+/-) time of Jesus' birth.
Does Luke know Matthew's story of the birth of Jesus and choose to tell it differently rather than independently?
Likely we will never know this side of glory!
Postscript: if Matthew and Luke are different, are they also contradictory? Obviously there is a long answer to this question which discusses each and every detail of difference and then draws a conclusion. A short answer is "not necessarily" because we could posit that Luke tells a story in Luke 2:1-40 which takes place before the sages visit (and omits any reference to the trip to Egypt which is consequential on their encounter with Herod) and Matthew 2 on the sages and the trip to Egypt, despite being the next verses after the birth at the end of Matthew 1, is a later set of events rather than something that takes place in the first weeks after the birth.