Pan-frying, sauteing and searing all happen in a pan or skillet, usually 3-6 times as wide as high. The differences between the techniques relate to the amount of oil used and the purpose of what you want to achieve.
This technique requires usually a good layer of oil in the pan. For example for frying fish, we use a good layer of oil surrounding the lower halve of the fish. Turn the food half-way the cooking process.
This technique most of us will use quite often, as a very versatile cooking technique. We apply it to cooking meat, fish, eggs, pancakes as well as vegetables. Apply a small amount of fat or vegetable oi to prevent charring and preventing the food from sticking to the pan. Using a thicker bottomed pan is preferred as more heat can be provided and the heat is better distributed over the pan surface.
Food items that release their own fat, such as bacon or duck breast, do not need any additional fat. Teflon or non-stick coated pans are very suitable for frying at relatively lower temperatures. Eggs and pancakes can be fried essentially with a bare minimum of oil in such pans.
This technique comprises the browning of the surface of meat or fish steak. To this goal we expose the food surface for a limited time to a very hot pan surface. And usually we do not add oil. Either we oil the food surface or we brush the pan surface with a little oil or fat.
For frying thick steaks of meat, we prefer a cast iron heavy bottomed pan. First we place the pan for 30 minutes in a hot oven to preheat. Thereafter we place it on high fire to quickly sear the steaks on both sides and to develop full flavor from the searing process. Then we place the pan with steaks back in the oven for a few minutes. Thus we reduce further browning of the outside, but cooking the steaks more from the inside. By doing this we create the right amount of cooking time to obtain the right desired done-ness. This approach prevents the steaks becoming black or charred from the outside.