As noted, there are a lot of variations in differing Christian traditions. The Great Schism in which the Roman/Latin/Western church was severed from the Eastern churches resulted in a break of communication so that the traditions are often different between them. Earlier traditions did not necessarily celebrate the Birth of Jesus (on Christmas or any other day), with some traditions celebrating the Epiphany, instead. That celebration maintained in the East long after the West had shifted the primary celebration to Christmas.
Further, the Reformation caused more rifts in the West. In particular, (for English speaking countries), the Puritans stomped out all celebration of Christmas and the various denominations (including the Anglicans) re-established different traditions at different times.
In the Catholic tradition, at least from the late Medieval period, Christmas began on December 25, (prior to that is the season of Advent which is a penitential/preparatory season sort of like “Lent lite”). The Christmas season then extended for forty days until the feast of the Presentation in the Temple. For whatever reason, the practice of blessing candles on that day arose, leading to the (re)naming of that feast and the close of the Christmas season on Candlemas.
A liturgical season determines the colors of the vestments worn and prayers recited at liturgical celebrations, so the Christmas season indicated the period during which the vestments were white and not some other color along with the themes of the prayers.
At some point, the extended Christmas season fell into disuse and the season was shortened to end at the feast of the Epiphany. In very recent years, that feast has been arbitrarily set to the second Sunday following Christmas, regardless on what day January 6 falls. (The denomination that most closely parallels the Catholic calendar is the Anglican Communion, but I do not know how much juggling of their calendar has occurred while Rome moved all their celebrations to convenient Sundays.)