For escargots, land snails are used. Most common are the species Helix pomatia, Helix aspersa and Helix lucorum*.
There are two restrictions: it should be edible (problem solved if you work with one of those three) and it should be large. Larger snails have more flesh to work with. You have to be a bit lucky for this. There's quite some variation. I think - for the dish that you mean - the snails should still have their house as well. However, I wouldn't advice you to go into the 'wild' and pick your own. Just buy them at the supermarket. It's safer, since snails can have digested toxins that take some time to leave their bodies.
The word "escargot" is French for "snail". You can find different preparations for snails, they would be called "escargots à la ..." with ... being the name of the sauce or preparation. The standard (at least here) drops the last part, since it's the basic preparation (herb butter with garlic).
There are other types of snails/slugs that are edible, for instance common whelks are also sold and eaten here, they live in the sea, not on land, but it's a whole different preparation.