I would say that if you went to the regions where they originated, you would find as many different variations of them as you do bbq here or tacos in Mexico or shish kabobs in Turkey, etc. And they would probably find it amusing that we are over here arguing about it on a bbq forum. Gyros, doner, shawarma are all pretty much regional variations of the same thing, along with tacos al pasteur in Mexico that simply started as copies of shawarma made by middle-eastern immigrants. I doubt if every traditional Greek dude making gyros at home has an elaborate vertical rotissarie spit setup, either. I like them both ways. My current favorite way to make gyros at home is with deer meat sliced paper-thin. I save a few deer roasts every year just for slicing into gyros and Phillie deer steak meat.
...Half a yard full of crap to cook on like everybody else...
Just a hungry hillbilly lookin for a dead critter to cook
in one throwdown,