1) There is no confusion -- the physical and nutritional calorie are the same thing (EXCEPT that the nutritional calorie is usually the kilocalorie, or Calorie with a capital c, while the physical calorie is the plain old calorie). You have to remember that the calorie is an abstract unit.

The human body is a gigantic chemical engine, but it operates in a different way from a (jet/propulsive) engine. It's like the difference between LiOn and NiCad batteries. You measure them both in volts or wattage output or hours, but they operate in fundamentally different ways -- you can't use the same chemical mixtures, even though those mixtures have the same potential energy as measured by some abstract unit.