Atheists don't derive their morals from these stories, that's the difference. That there is some superficial overlap (a tree? presents?) doesn't allow you to claim the morality of atheists as religion-derived. That's ludicrous. It's like saying the local butcher taking apart a pig is adhering to Aztec rituals and their morals because at some point in both 'ceremonies' someone holds a heart in their hands.
In fact, the source of morals among atheists seems to be a permanent puzzle for many people with religious background, simply claiming them as religion-based misses the point completely.