I put 1 tablespoon of oil in an iron Kadhai. Then after it gets a bit heated, I put a chopped onion in it, and start moving it with spatula so that it doesn't get burnt and gets cooked evenly.
So, what am I doing, stir frying or Sautéing?
It mostly depends on the heat used. If you are cooking at a high enough heat that vegetables and thinly-sliced meats (if using) are cooked through in only a few minutes then it matches with the term generally used as "stir-frying". In this heat, if you stop stirring even for a moment, pretty much, the food at the hottest part of the pan (at the base, near the flame) will start to burn. It needs to be in motion constantly.
That's the stir part of the stir-fry -- constant motion up the curved sides where it is cooler and letting other parts of the food go to the bottom to the heat and around and around. A full dish of meat, veg, noodles, etc can be completely cooked start to finish in just about 5 minutes.
Sautéing should also be at a fairly high heat and generally with less oil (although stir-frying doesn't use a lot of oil either, usually). The heat is lower than what is implied by stir-fry. With sautéing you are still generally keeping things moving, but it doesn't need to be quite as frantic. You can let things stop a moment, and it can help to let them start to brown and caramelize.
To demonstrate, this recipe for sautéed baby bok choy cooks them for 7 minutes, this one for 9-11 minutes, this one is another outlier cooking it for 4 minutes. The fastest of these is twice as slow as most of the the stir-fry or about the same as the slowest stir-fry. The slowest of these sauté recipes is nearly 3-5 times as slow as the stir-fry with fairly similar ingredients, especially similar to the slowest of the stir-fry recipes.
But to be fair, in my comment on the other post I was, strictly speaking, abusing the term sautéing by conflating it with even more moderate temperatures (which are more properly simply called "pan frying").
A kadai is a good implement to use for stir-frying, but a kadai can also be used for cooking at a slightly lower temperature. Simply using a kadai does not 100% determine the end result will be either a stir-fry or a sauté or a gentle fry, or even deep-frying. It's a versatile vessel. :-)
The (unsupported) assertion you quoted is a bit extreme. Stir frying and sauteing are roughly analogous - both involve cooking in a pan over a high heat with a small amount of oil by constantly moving the food. The only real difference is that stir frying usually involves a wok, and higher heat. Sauteing is usually done in a saute pan and the heat is usually less fierce. But they are basically two sides of the same coin.