Sautéing vs Frying vs Caramelizing -- what's the difference?

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.

I would argue the difference between sautéing and pan frying is in the movement of the pan.

Sautéing comes from the french, sauté meaning to jump. So sautéing is very much a western form of stir-frying.

For pan-frying I generally think of eggs, steak, etc, where the food is put into the pan and left, perhaps being flipped once or twice, but otherwise static.

To me, frying can be two things, pan frying and deep frying. Deep frying is using a lot of fat to completely cover the item in question. Pan frying usually implies larger items such as meats (imagine a breaded chicken cutlet or a nice steak). Sautéing usually implies smaller items (onions and peppers). Some people differentiate the two by the amount of fat used - sautéing would have less, and pan frying slightly more. In most cases, you can use the terms pan frying and sautéing interchangeably and get your point across. Both need relatively high heat.

Caramelizing, on the other hand, is what you're doing. Caramelizing is generally "low and slow" - low heat, for a longer period of time. If you're extracting a sweet flavor from the onions, that's almost definitely from caramelization, the extraction/oxidation of the onion's natural sugars.

Edit: As yossarian pointed out, caramelizing is a process that can occur when you sauté or pan-fry.

In my opinion, "Frying" is the term used when using oil (canola, olive, corn, etc.). and "Sauteing" is the term used when using butter. The heat differences are valid points, but I believe it comes down to the type of fat used.