Shawarma (the closest English translation to the Arabic) is all of those things, and more. Some think of shawarmas as the "Arabian Taco," because of their ubiquitous and inexpensive nature.
People also think of Shawarmas as being similar to Gyros (from Greece), this is not true: the Gyro, excellent in its own right, usually has different ingredients inside the sandwich. Gyro meat is often quite different as well, both in its spices and in that Gyro meat is usually a mixture of beef and lamb while shawarma is typically never beef and occasionally only lamb. In the states, most Gyros in restaurants come from the same company and the meat is a very particular flavor.
The shawarma is also a country by country experience, changing taste and texture even by neighborhood in the same city.
If you travel in the Middle East, you will invariably come across these delicious street-side items and will be surprised by the variety of them that you will find.
Most shawarmas are made outside restaurants, you can spot the shawarma shops by their massive towering logs of revolving meat and their vertical red cookers that are sizzling the rawness away. These meat towers are usually manned by shawarma cutters, sometimes dressed in entire cooks outfits replete with French chef hats. The men wield lengthy knives with which they slice off bits of the meat into a receptacle. These hearty souls are usually drenched in sweat, being outside in the Middle East weather, fully dressed, and standing before searing hot cooking grids.
Some countries like the UAE have banned outdoor shawarma cooking due to health concerns, unfortunately, so now the cutting men have to stand inside makeshift outdoor shed type houses which undoubtedly adds to the heat (it can get up to 130 degrees F in some Gulf Countries, even at night).
The receptacle that the meat falls into is also usually home to some of the shawarmas toppings, such as sliced tomatoes, onions or cucumbers. This allows the vegetables to soak up the meat juices from above, giving them a very distinct taste.
Most shawarma is made with lamb or chicken, though you can have a lamb/beef mixture, even goat.
What else goes inside is a matter for the restaurant. The best shawarmas in Abu Dhabi were made in small pita breads which were sliced open and included tomatoes, garlic sauce, pickles, tabouli, and french fries (of all things).
In Syria and Lebanon they come wrapped up in a flatbread not unlike a Mexican tortilla.
The entirety (if on pita) is then rolled up like a taco and put in a wrapper.
Falafel is sometimes served like French Fries, on the side, with some tabouli (instead of ketchup). Turnip pickles (the french fry looking purple things) are another delicious side dish usually served.
