How is fat diet different from a low calorie diet

Fat is one of six nutrients your body needs to stay healthy. The other five nutrients are:

Carbohydrates (found in fruits, vegetables, pasta, rice, grains, peas, beans, and other legumes)
Proteins (found in meat, poultry, dairy products, eggs, and beans)
Minerals (such as potassium, calcium, and iron)
Vitamins (such as vitamins A, D, E, and K)
Water
Of these six nutrients, carbohydrates, protein and fats provide calories. Each gram of carbohydrate and protein yield 4 calories/gram. Each gram of fat yields 9 calories.

A calorie is a measurement, just like a teaspoon or an inch. Calories are the amount of energy released when your body breaks down (digests and absorbs) food. The more calories a food has, the more energy it can provide to your body. When you eat more calories than you need, your body stores the extra calories as body fat. Even a fat-free food can have a lot of calories. Excess calories in any form can be stored as body fat.