Originally Posted by Wiseman Silo
Now that is a nice way to explain it. So it does go back to my original comment its HOW the damage is delt. Katarina though seems to be the one exception.
What makes her not a mage if she is indeed an AP carry. Whats the dfiference between mage and AP carry? Item dependency? Thats what i always figured an AD carry was someone who can carry the team but needs the farm and needs higher end items earlier to be effective like Caitlyn or Ashe.
I consider the term 'mage' to mean 'anyone that uses ability power items and does magic damage'.
Within the category of 'mage' there are several roles to play though. You're either sustained dps (Ryze and Cass), AoE burst (Brand, Annie, etc), or an assassin. A few don't fall into any of these categories since they have weaker overall teamfight damage, but more utility in form of buffs, or poking ability etc. This I would class as supportive DPS (like Nidalee, Zilean, or AP Janna).
And yes, I am aware that Katarina can be built for AD if the user so chooses, as her Q and ult both scale with AD as well. However, AP Kat is the more common route.
AP carries carry the team by bursting the enemy team for a significant chunk of health. AD carries carry the team by dealing consistent high damage damage. In an ideal world this means the AP carry blows their combo once the teamfight breaks out, and the AD carry mops up.