Yes, that is the thing. Mexican cuisine is not monolithic. The authentic stuff uses whatever they have locally, so it varies from region to region. And you only have to go literally one or two blocks away from the tourist areas to find it.

I don't recall precisely which birria they served. It was this place (I copied the link displaying the chalkboard):

Google: Maps Uv

Could have been either. Really good. One block off the main drag. We went twice. Once, we were the only non-local people in the joint. The other time there was another white couple having even more difficulty communicating than I was (mi español esta muy rustico). We make our birria (well, 1poorlady does it) from beef. She went hunting for a recipe after we got back from Cabo, and found a good one.

I'd have to check my notes, but I think if we go to Oaxaca that we need to get their mole. Could be wrong, but I think that's one of the famous dishes.

One of my favorite local Mexican places in our area features Jalisco cuisine. Family run. Been a while since we visited as we have more time to cook ourselves (since retirement). Our old favorite burned down several years ago, and apparently they didn't have insurance to rebuild. La Tolteca. Really good, but, alas, no more. I met Loren there when he was in town.

I still maintain that Taco Bell is no more Mexican food than Panda is Chinese food. I've been to Taiwan, as well as a couple of restaurants that have "authentic menus"**, and Panda isn't really Chinese. Maybe "Chinese style". If you like Taco Bell, cool. Just know that it is not what you would get south of the border. Or even in many places in Arizona and other border states. You'll not find tripa or lengua on the menu at Taco Bell. ;-)

**When they see 1poorlady, those that have separate menus will ask if we want one. Which we do. Their default menu is Americanized Chinese. Lots of breading and wok fried.