The green sauce is not in packets or anything. It's just called 'green', like the stuff on a regular tostada or a bean burrito is 'red'. It appears to be just chopped skinless green chiles, with maybe a thickener, no mayo. It's kinda clear looking and not very spicy -definitely not jalepeno. I just order something like 'a bean burrito with green sauce please' and the cashier does:
on the receipt. Once in a blue moon I get asked if I want the green in addition to the regular red sauce.
I learned about the sauce in Santa Fe, where everywhere you eat people ask if you want 'red or green' so, I never learned a fancy name for it. No one has ever not known what it is. That said, I have mostly been living in the SouthWest.
It was originally on the quesadillas, back when they were introduced around 1997 or so (?) then a couple of years later they changed to the creamy sauce. I prefer the green. It's also really good on the breakfast crunchwrap, there's a slight acidity to it that really changes the dish. (I also have less of a tendency to feel overstuffed, so I think it has less fat than the creamy sauces)