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Not the same but very similar.
What’s the difference between a gyro and a shawarma and Why Do People Confuse Them?

At first glance, gyros and shawarma look like the same thing. The meat for both is shaved from a large cone that slowly turns and roasts all day, cooking the meat in its own juices. And below this surface of similarity, the two meals share a common ancestor: the doner kebab. Invented in Turkey in the 18th or 19th century, doner kebab means “rotating grilled meat.”

When it was introduced to Greece, the locals named it “gyros,” the Greek word for “turn.” Likewise, when it spread through the Middle East, it was called “shawarma,” an Arabic word for “turning.” Of course, if you’ve ever seen the meat spinning on a rotisserie, you understand why these names stuck.

The Gyro is a Greek dish and usually uses a combination of ground lamb and ground beaf. The meat is seasoned with a blend of oregano, rosemary, thyme and marjoram and made into a loaf and cooked on a tall spit. The garnishes comprise tomatoes, onion and tzatziki sauce, a yogurt sauce seasoned with cucumbers and dill and sometimes garlic.

The Shawarma’s origins, on the other hand, are less definitive, but essentially Middle Eastern. The meat is usually lamb, chicken or turkey and consists of chunks of meat (rather than a ground loaf). The seasoning is also quite different and is based on turmeric, cardamom, cinnamon and cloves – with many different variations on this basic mix.

However, what really sets the shawarma apart from the gyro is the garnish, or rather, the extent of the garnish. The Israeli shawarma, for example, offers generous servings of hummus, tahini and, perhaps most important, pickled mangoes.