If you ever wondered what in the heck the difference between these things like I have, then you should check out the discussion at chowhound. There are so many posts about the topic, but now I think I get it. Here is one of the many posts.
Donner, Shwarma, and Gyro all refer to the way the meat is cooked - upright on a spit. This method of cooking orignated in southern Turkey and was refered to as 'chevirme', meaning "rotation," or, "turning". 'Chevirme' was pronounced 'shwarma' by Arabic speakers. Similarly, 'doner' comes from the Turkish verb 'donmek', meaning "to turn". This cooking method is referred to as 'gyro' in Greek, meaning "to turn," also (think 'gyroscope'). Doner/shwarma/gyro probably originated in southern Turkey and was quickly adopted into the cuisine of northern Syria. By and large, upright roasted meat is an Anatolian, Levantine, and Greek tradition. The regional differences in all of these dishes stem from the local fixings that are served with them. In Aleppo (my personal favorite), for instance, it tends to be quite spicy, served with pickles, and after the meat is rolled in the bread with the fixings the whole thing is dipped in the drippings and toasted on a griddle. Turks tend to forgo the dip in fat and use creamier fillings (though this is sometimes seen in Syria as well). Greeks tend to slather theirs in the ubiquitous tadziki. by Trencherman