There are 2 Bethlehems in Israel.
The Old Testament prophesied that Jesus would be born in Bethlehem Ephratah.
Micah 5:2 But thou, Beth-lehem Ephratah, though thou be little among the thousands of Judah, yet out of thee shall he come forth unto me that is to be ruler in Israel; whose goings forth have been from of old, from everlasting.
It's the same Bethlehem where David was born.
Luke 2:4 And Joseph also went up from Galilee, out of the city of Nazareth, into Judaea, unto the city of David, which is called Bethlehem; (because he was of the house and lineage of David:)
Bethlehem Ephratah is also known as Juda.
1 Samuel 17:12 Now David was the son of that Ephrathite of Beth-lehem-judah, whose name was Jesse; and he had eight sons: and the man went among men for an old man in the days of Saul.
Matthew 2:6 And thou Bethlehem, in the land of Juda, art not the least among the princes of Juda: for out of thee shall come a Governor, that shall rule my people Israel.
It's the same Bethlehem referenced, where Jacob's wife Rachal was buried.
Genesis 35:19 And Rachel died, and was buried in the way to Ephrath, which is Beth-lehem.
The birthplace of Christ was Bethlehem Ephratah, which is also referenced as:
"City of David" in Luke 2:4
"Judah" in 1 Samuel 17:12 & Matthew 2:6
"Ephrath" in Genesis 35:19
The other Bethlehem is north in the territory of Zebulon, which is also known as Bethlehem of Galilee. This is not the Bethlehem that references Christ's birthplace.