Why 월계수 instead of 계수?

Today, while reading a story about the Olympics ("올림픽 이야기") on the Korean Lab Web site, I came across the word 월계관, which was the laurel crown traditionally given the the winners of the Olympic games. I looked up the word and found that it was made from a "bay tree," which is a broadleaf (활엽수) evergreen (상록수) that grows in the southern part of Europe and along the Mediterranean coast. In Korean, a bay tree is called a 월계수(月桂樹), which is why a "laurel crown" in Korean is called a 월계관(月桂冠). 관(冠) means "hat" or "crown."

Here are the individual Chinese characters for 월계수(月桂樹):

• 月(월) moon
• 桂(계) a Katsura tree
• 樹(수) tree

As you can see from the Chinese characters above, the literally meaning of a 월계수 is "the moon Katsura tree," which makes this word a little strange. Why call it a "moon Katsura tree" instead of just a "Katsura tree" (계수나무)?

There is a Korean story that talks about the moon, rabbits, "the elixir of life," and a Katsura tree. Here is a link to the Korean story, and below is my translation:

Rabbits Pounding Out the Elixir of Life

Longer than a long time ago, God lived in the broad sky and ruled the heavens. The grandfather of Tangun, the founder of our country, is this very same God. In the heaven that God ruled there was a wonderful medicine called 불사약 (elixir of life). If you took this medicine one time, you would feel happy for one month. If you took it two times, you would not get sick. And it you took it three times, you would never grow old and would stay young.

One day the elixir of life was stolen, and God contemplated agonizingly, "How can I prevent further thief and safely produce the elixir of life?" Finally, he decided that it would have to be produced it in a place that no one could go.

"Where would be a good place? Of course, it could be produced on the bright moon, at night when everyone is sleeping. But who should I send to make it? I could send rabbits. Rabbits are not lazy and would work hard to make the elixir."

After deciding on his plan, God sent rabbits to the moon, together with a wonderful mortar to make the elixir of life. The rabbits really did work hard pounding and making the elixir. God caused a huge Katsura tree to grow, so that the hard working rabbits could pound out the elixir of life under the shade of the tree.

Look up at the moon one time. Can you find the rabbits pounding the motar under the Katsura tree? You are not sure?

My question is this: Why is the tree in the Mediterranean called a "moon Katsura tree," but the tree in the Korean story is called just a "Katsura tree"? It seems like the names should be reversed? Maybe because Koreans learned of the tree in the Mediterranean later and could not give it the same name as the tree in the story since they are different trees?

Here is a link to a picture of the rabbits working on the moon under what is supposed to be a Katsura tree.