I would assume that they're the same type of mystery snails (or apple snail, which is just another name for them). Mystery snails are air breathers like bettas, so I assume that's why they're not in a tank like the snails you typically see in aquariums, but the ones that are kept at my petsmart are in fully submersed tanks with room to breathe.
One of the things you should first test is the pH of your water if you don't know it already. One of the driving factors for snails is a pH around 8.0 although 7.0 is, I believe, the minimum..... Otherwise, it helps to have tests for GH and KH, which if you don't know what that is just yet, it's for general and carbonate hardness....
Make sure you provide calcium as well. You can do this by either giving it calcium enriched foods or seperately giving it calcium tabs; which you can actually use ones taken orally by people.
If you have any problems of any sort or would rather get more information about apple/mystery snails, then applesnail.net is a wonderful website to go to. Sometimes they're a bit slow on responses in the forums, but I suppose that's expected for snail lovers xD lol....