A mage can cast spells from afar a melee has to be next to the boss to hit it. Probably why one of the reasons they have to stand still when they cast.
Moving and casting has nothing to do with animation lock. only spells with no cast time can be cast if you're already moving anyway- casting time keeps mages in one spot regardless of whether animation lock exists. Mages are more vulnerable and have to be really careful in PvP.