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.