There are actually quite a few which makes it confusing: Shawarma, Shish Kebab, Shish Taouk, Döner and Gyro.
The differences are how they prepare the meet, the spices used, the toping ingredients and the region they come from. As someone said, it used to be my favorite after clubing food when I was in my 20's. They all taste yummy!
In Quebec city we have this 24 hours restaurant named Beyrouth Cité, it's pretty good.
Region doesn't have much to do with it. No matter where you go, Shish Taouk is chicken, Shish Kebab are blocks of meats (beef or lamb), and Shawarma is cut in slices. All have their own unique marinade and spices.
That's the traditional way.
After clubbing spots, fast food joints, they usually do doners, which simply means ''rotating'' in Turkish, hence those massive chunks of meats rotating and getting grilled.
Doner is turkish, Gyro is greek. They mean the same thing, the difference usually comes from having more greek ingredients, ie, tzatziki, greek bread, greek spices, for the gyro, and the doner is more middle eastern style.