Christmas Carols: What does that mean? #2- We three kings from...the Orient?

I was always confused by the line in the Christmas song We Three Kings which said they were from the Orient.

We three kings of Orient are;
Bearing gifts we traverse afar,
Field and fountain, moor and mountain,
Following yonder star

Refrain:
O star of wonder, star of night,
Star with royal beauty bright,
Westward leading, still proceeding,
Guide us to thy perfect light.

The Christmas carol was written by John Henry Hopkins, Jr. in 1857. We truly do not know how many kings visited Jesus in His nativity nor for certain what country of origin from which they traveled. Traditions says Persia.

However since the scripture in Matthew 2:1 says they traveled from the east, then since the east in that time up to now has been called the Orient, then, the Orient it is.

I'd always thought the Orient meant Japan, China, Taiwan, Korea, etc. Isn't that the Orient? Is Persia, Syria, or even India, Pakistan, and Afghanistan the orient? Yes, and no. According to Wikipedia,

The Orient is the East, traditionally comprising anything that belongs to the Eastern world, in relation to Europe.

The term "Orient" derives from the Latin word oriens meaning "east". ... Also, many ancient temples, including pagan temples and the Jewish Temple in Jerusalem, were built with their main entrances facing the East. This tradition was carried on in Christian churches. To situate them in such a manner was to "orient" them in the proper direction. When something was facing the correct direction, it was said to be in the proper orientation. (Source)

The Easton Bible Dictionary defines biblical use of east,

The orient (mizrah); the rising of the sun. Thus "the east country" is the country lying to the east of Syria, the Elymais (Zechariah 8:7).

(2). Properly what is in front of one, or a country that is before or in front of another; the rendering of the word kedem . In pointing out the quarters, a Hebrew always looked with his face toward the east. The word kedem is used when the four quarters of the world are described (Genesis 13:14 ; 28:14); and mizrah when the east only is distinguished from the west ( Joshua 11:3 ; Psalms 50:1 ; 103:12 , etc.). In Genesis 25:6 "eastward" is literally "unto the land of kedem;" i.e., the lands lying east of Palestine, namely, Arabia, Mesopotamia, etc.

Whether you are from the Orient or the Occident, we celebrate the Savior's birth who threw away our sins as far as the east is from the west. (Psalm 103:12).