The variety is just that, green chile. It is a specific type of pepper. Now, if the recipe calls for Hatch green chiles, it would be referring specifically to the green chiles grown in the Hatch valley of northeren New Mexico. Any other type of pepper will be identified by it's name, such as Anaheim, jalapeño, cherry, New Mexico, serrano, poblano, fresno, habanero, etc.
Now, if the recipe calls for DICED green chiles, I would have to assume it is referring to the canned product, available from most Latino food manufacturers such as Ortega, Las Palmas, Rotel, and yes, there is even a Hatch brand out there. Check the Mexican, Hispanic, or Latino (depending on which is the most popular term where you live) foods aisle of your regular grocery store.