Difference between Pan-Frying and Searing

I've never really considered there to be a real difference between sautéing and frying. They both mean to cook in a hot pan with a little bit of fat. However there isn't a lot of consistency online. It doesn't look like there's any sort of definitive answer here. Some points of view:

• They're the same, although frying might involve slightly more oil. The terms are essentially interchangeable. This is the top hit on a google search "sauteing frying" (although this question is on the first page!).
• As Aaronut says, sautéing involves jumping the food while frying involves a little more oil and less flipping or stiring of the food. Here's another source for this definition. This definition makes a delineation between pan frying and shallow frying.
• Frying is the same as shallow frying and involves partially submerging the food in oil. Food is normally breaded first. There's no distinction between frying and shallow frying. This is Martha Stewart's definition.

As you can see, it's really all over the map, and that was just from the first page of the google results. I think we're getting in to issues with language changing beneath us. However, I think the safest bet is probably that sautéing involves a lot of stirring, frying doesn't, and I should consider refining my own definitions.

Caramelizing (which fortunately doesn't have any of the same confusion) is a process that happens during cooking when sugar oxidizes. There are many different ways that you can achieve this effect. One of the ways is to sauté or fry (depending on your definition) something until the water sweats out and the remaining sugar heats up.

So the answer is that you are caramelizing the onions by sautéing (or maybe frying) them.

If you are looking to fry veggies then yes, it is necessary to pre-heat. If you put them in a cold pan with oil, you start 'sweating' the veggies instead of frying them.

For example: if you put a sliced onion into a pan with hot oil, it will cook and have a nice golden brown color as it caramelizes. Put that same sliced onion in a cold pan with cold oil and then add heat, and the onion will first turn translucent and lose moisture.

Both of these cooking methods have their uses, but they are different.
How do you know when the oil is ready to cook? It will start to shimmer a little before it reaches the smoking point. Put the veggies in when you see this shimmer, or at the very first wisp of smoke.