The game confuses "magic" and "magic" --- apparently Blizzard failed to establish a list of terms for the game, so some developers used "magic" for magic, or elemental, or both.
That's what you get when you try to cut down the paperwork
As far as I know, "magic damage reduced" includes magic and elemental.
As a side note, it was even worse with a translated game I played long ago (never playing translated games anymore), since apparently they used several translators without (again) establishing common ground. This made NPCs talk about monsters that didn't exist in the game at all, since the monsters themselves had different names... which did cause problems for me since I was looking for that quest and couldn't find the monsters they were talking about...