Vegetable oil is an all-purpose catchall term for a neutral flavored oil, if not otherwise indicated, usually soybean oil or a blend. Canola and corn oil are also vegetable oils.
Some olive oils are pretty neutral, others can have a strong flavor and shouldn't be used for baking unless the recipe calls for olive oil.
Applesauce is a great low calorie substitute and works great in some recipes, but not so well in others. Also, things made with applesauce will dry out more quickly, as oil is one of the ingredients that makes baked goods moist.