The Hebrew word used in this case is ṣemaḥ (also spelled as tsemach, tzemah or whatever else is in between). Traditionally this is translated as “branch,” although this might not be the best word to render it to: since tzemah is related to the Hebrew verb meaning “to sprout” or “germinate” (basically something growing up, sprouting out of the ground), alternative renderings include ‘(off)shoot’ or ‘sprout’.
The thing is, in the Greek translation of Zechariah, the translator apparently took the ‘rising’ connotation of the original Hebrew verb and switched the organic metaphor to an astronomical one: from a plant ‘rising’ from the soil to a star or the sun ‘rising’ in the sky. The translator rendered tzemah into the Greek word anatolē, “rising,” “dawn” or “east.” St. Jerome, although he was translating from the Hebrew, followed the Greek translator’s choice of words at this point, hence oriens.
Around the time of Jesus, tzemah has become an established title for the Messiah: the Greek interpretation of the word, anatolē, has been connected with Balaam’s prophecy that “A star will come out of Jacob; a scepter will rise out of Israel.” You can see this application in the gospels: the star of the magi in Matthew, and that verse in Zechariah’s hymn (Luke 1:78): “because of the tender mercy of our God, whereby the sunrise (anatolē) shall visit us from on high.”
Regarding the Masoretic you mentioned (ṣemaḥ), my English mind can’t help but think of the word semaphore. From that word semaphore, although this is just for fun, the Greek σῆμα means sign and φέρω, phero, means to bear: the sign-bearer. Interesting.
Ver. 12. Orient. Protestants, “the branch, and he shall grow up out of his place.” (Haydock) — Hebrew, “under or from himself.” This alludes to the miraculous birth of Christ, (Isaias xi. 1.) whom the prophet had principally in view; though his hearers might naturally understand (Calmet) Zorobabel, who was to preserve the royal family and build the temple. (Theodoret; St. Jerome) — Yet he was only a shadow of the Messias, chap. iii. 8. (Calmet)
Patrick partially explained the Hebrew. It means that which rises from the earth. I believe this is with word in the Hebrew the people used for the planet Venus, translated anatole in the Greek which Jesus identifies with Himself in Revelation 22:16 Jesus identifies Venus with Himself as the bright Morning Star. Venus is the one star that like the sun and the moon could be seen immediately as it rose rather than being invisible until it rose five to ten degrees about the earth due to extinction (the anmosphere near the horizon dims the stars light).
Luke 1:78 Translated dayspring in the KJV. If anatole is in the plural it refers to the direction east, if it is in the singular it refers to a heliacal rising of a star. That is something that rises in the east with the sun. Orient refers to the direction east. I discuss this somewhat in my article on the star of Bethlehem here www.scripturescholar.com/VenusStarofBethlehem.htm
Grace and peace,