On the Food network they boil potatoes, but they poach carrots. They poach turkey, but they boil eggs. They sauté’ onions, but they fry eggs in the same pan. Likewise, they fry hash browns, but they sauté’ onions in the same pan before adding the potatoes.
I can go on for days.
For saute vs fry the big difference is movement. Frying means let it sit, generally flip it once per side a food can supportitself on. Saute means near constant stirring or agitation.