there is a lot of debate on exactly when Jesus was born and died. There is no evidence of any particular birthday, other than lambing season (spring - not Winter solstice). We can narrow his Birthday down to about a dozen years based on events, and darkness for 3 hours at his death seems to describe an eclipse which also narrows things down. From that most experts now think his birth year would have been year 4, but there is a lot of debate.

We know the day of his death on the Hebrew calendar (end of Passover - often called Easter), but the Hebrew calendar is weird with extra months added some years when needed to match the moon phases to the seasons. Different towns could choose different years for that extra month though, and so we have no clue how to translate that to a modern calendar system. Which is why Western Easter and Orthodox Easter are not always on the same day.