Well, I kind of sort of have to go with TB on the "fajita" 'thang, but only in a kinda sorta way. And I guess I also kind of sort of have to go with THP, but also only in a kinda sorta way. Though, really, I don't entirely care what you call what, as long as I know what I'm getting. If you tell me you're serving me something called "a pickle" and describe it as "lobster blah blah blah", I'm cool with that. I'll order your "pickle" and know I'm getting lobster.
For me (and keep in mind this is from living in Houston more than half my life), "fajita" is still grilled skirt steak if it's considered to be a "beef fajita", and no one has to describe a cut for "chicken fajita" or "shrimp fajita". But over and above a cut of beef, "beef fajita" for me has a certain blend of seasonings. "Carne asada", on the other hand, is (for me) a big hunk of ribeye, open-flame-grilled to perfection with a different flavor profile. Even though "carne asada" just translates to "roast beef" in English, it's not carne asada to me unless it's thick and open-flame-grilled ribeye. Also, places around here serve god-only-knows-what-cut (could be any and actually includes ribeye) as almost paper-thin like they're trying to mimic fajita slices and even "grill" them on a flattop. Fact is the eater can slice up carne asada and wrap and eat it just like a fajita, but again, different seasonings. Then we get to "barbacoa", which to me is more just barbecued, shredded beef and the cut is less important as long as it's one that takes a low, slow grilling. If you want to call a big hunk o' open-flame-grilled ribeye "barbacoa", go for it. Like I said, all I really care is how you define your words, not what names you assign.
But JayWOW and others, if you wanna oven-cook your tacos, fajitas, and anything else, go for it. Mostly I just see that as drying out the tortillas, but if you wanna, I don't mind.