Markse,
A little more more information could help really nail it down for you.
Empanadas aren't just basically turnovers, they are exactly turnovers. They're made with a wheat-flour dough that's like a savory pie dough (you could use pate brisee, no problem) and completely unlike "tortilla dough."
Tortillas on the other hand are made from a type of dough called masa -- which is also the name of the flour used to make it. Spanish is usually unambiguous. Usually. Pero lo siento, no siempre.
Sopadillas aka sopapillas are crispy beignet, sort of. They are South American, not traditionally Mexican (although you can find them in Mexican restaurants here in el Norte) are very seldom made with corn flour, and the dough is nothing like the one used to make tortillas -- whether corn or flour. Sopapillas are usually, but not always, sweet; and served for snacks or dessert.
So, while both are very good, I doubt either is what you're looking for.
I'm guessing sopes (SOH-pays) -- which would be a fried, stuffed, low-sided shell. Here's a pic, if that helps:

These are from King Taco in my part of the world. They're typical, but some sopes have higher sides and look more like a cup.
You can buy pre-made, raw (you buy, you fry) sope shells if you have access to a good Mexican market. They're extremely easy to make -- especially if you have access to a good Mexican bakery and can purchase great pre-mixed masa. Otherwise, it's no more difficult than making great masa at home. Which is mostly, but not entirely a matter of whipping the lard into the flour just right. If you weren't taught by your grandmother and haven't been doing for at least a couple of generations yourself... Good luck with that.
There are lots of variations of sopes -- sometimes but not always regional -- each of which has a different name. Or not. Were the ones you're asking about baked or fried? Open or closed? A stuffed shell with sides, or everything laid out on top? Round or oval? How many to make a meal?
One thing that's fairly constant: Sopes are almost always made from corn masa, not wheat. So if your neighborhood abuela's "pastries" were made from corn, there's a good likelihood we're talking one type of sope or another.
Also, sopes are by no means the only option. Any additional information you can give could be helpful.
Can I get an "Orale!"?
BDL
Edited by boar_d_laze - 7/26/11 at 7:44pm