As I understand it, all of these terms refer to cooking food in a small amount of fat/oil. What exactly is the difference?
Pan frying means letting the food sit in the pan and occasionally stirring or flipping. It tends to be done with larger pieces of food, and at a medium to medium-high heat.
Sautéing means shaking the pan back and forth - making the food "jump", if you're translating directly. It's done at a high heat, for a short time, usually with thinly-sliced or finely-chopped ingredients.
Shallow frying, according to some references, refers to the food being partially (halfway) submerged in hot oil and flipped once, as opposed to deep-frying where the food is fully-submerged the whole time.
I prefer the answer in wikipedia:
And it differs from pan-frying:
I've never heard of shallow frying...