Magician used to be a wise user of magic; such as the Biblical "Magi",and so is a witch. But over the years, the word magician has become much more associated with "conjuror", or "illusionist". Really the word magician is a bit derogatory now, which is a shame, but it is due to the changes that often occur in language. It is much like saying that Wicca is a religion, and witchcraft is merely a Craft. It doesn't make sense to me; I was a witch long before Wicca was ever heard of, and it was (and still is) my religion.
It is a peculiarity of the English language, it changes over time. The word "gay" meant happy when I was young; no longer!