They are indeed both part of the same family but just a different species. The family known as apple snails are ampullariidae and include several species: lanistes, pila, marisa, and pomacea. The last of which the is the species in which the "mystery snail" belongs to, pomacea bridgesii for those who care.
Edit: Sorry for all the technical terms but I just love research and tend to go overboard.
Ask at your local PetSmart or PetCo if they have any Pond Snails or Ramshorn Snails. If they sell live plants in a tank they probably have them. They are free, as they are considered pests. I saw two Ramshorns at my PetSmart today in with the mondo grass. I wanted them really bad, but I have no where to put them.