User blog comment:Hyperborean/"The House of Hades" – official expectations blog/@comment-5839833-20121211134848/@comment-3146930-20121222135335

Well you're talking about a planet that in it's long history has about 3000 recorded gods, so obviously some areas are going to overlap. When Percy, Grover, and Annabeth visit the Underworld in The Lightning Thief, they see a priest there and Grover mentions that he could be seeing what he sees as hell, not necessarily the Greek Underworld. However, based on the logic of the world of Rick Riordan, any mythology could be real. The most obvious answer is that you will go to any afterlife you believe in the most. The priest most likely saw hell as a place of fire and pain, which does match the description of the Greek Underworld, he may just see it as the Christian hell.