What's the relationship between Jesus and Horus? Are they one and the same, or close relatives? I have heard that the Christians borrowed from Egyptian mythology.
There is no relationship at all. Horus is often depicted in Egyptian art with his mother, Isis. The old mother and child motif. Now that’s a really common theme in art! So the fact that they are both depicted with their mothers is nothing but coincidence. Here is a comparison between an ancient Egyptian statue and a medieval Christian painting. As you can see, we don't need the ancient Egyptians to imagine the source of the Christian depiction: everyday life.
For more on supposed parallels between Christ and ancient mythology, please listen to the Apocrypha lesson (class 4) in How the Bible Came to Be (podcast series). Or read the Gospels chapter in Compelling Evidence. Or read my response to Zeitgeist. Hope these resources help.