Christianity subsumed some pagan traditions. It's hardly a secret "gotcha", it's open for all to see. In the same way that when I eat an apple, the apple becomes part of me, I don't become an apple.

There are critical differences between Paganism and Christianity. For example, the philosopher Rene Girard showed that many traditions had stories of mimetic desire and scapegoating, but Christianity showed the crucial end of that story, the fact that the killing of the scapegoat to save the community is a lie https://www.youtube.com/watch?v=LSzF2OG2ejI.

GK Chesterton has a lot of interesting things to say about Pagans also http://www.online-literature.com/chesterton/heretics/12/, and his book The Everlasting Man is worth reading for the way that it uses pagan tropes to point towards Christianity.