I'm comfortable excluding wraps and burritos, but I think gyros fit the "two distinct halves" criterion. Although the thickness is uniform, unlike a hot dog or sub, when holding a gyros there are clear sides that function much like a sub. The wraps and burritos are excluded because one could turn them in any direction without losing the contents.It excludes wraps, burritos, gyros
The issue is that the "clear sides" of a gyro are made up of one piece of flatbread that's folded around some meat and veg. A gyro is essentially a wrap that doesn't wrap around all the way. Sure, it has distinct sides. But I challenge anybody to find the top and bottom halves of a gyro. The crucial difference between hot dog buns, sub buns, and other things similar to them is the cut. The cut gives the bun sandwich-like definition. A fold can approximate it, but a folded piece of bread is inherently unstable. It needs to be held shut, or it reverts to just "flatbread with toppings". You can complete the fold by rolling both sides together - but then you're back at a wrap again. Good points though. If I can find a better definition, I will.