My guess is that what you call "apple snail" is a Pomacea canaliculata or something similar, while the "mystery snail" is a Pomacea bridgesii. They have differently shaped shells, see the bottom of this page for drawings:
http://www.applesnail.net/content/species_genera.htm
But here are the main differences:
* Pomacea bridgesii come in many more colors (while, blue, yellow, pink, purple, brown, tan; striped & plain), while the Pomacea canaliculata usually only come in yellow (although I have seen for sale a brown striped one)
* Pomacea canaliculata get much larger. My Pomacea bridgesii get to a max shell diameter of about 1.5". I'm not sure of the max size of the P. canaliculata since I've never had one, but they are supposed to be quite a bit bigger.
* P. canaliculata EAT PLANTS which is why I've never owned one (all my tanks are planted). P. bridgesii don't, except for duckweed which they love.
Below is a picture of my now sadly departed (they don't live very long) P. bridgesii "Grape"
