calories is the amount of energy dervied from the food we consumed. fat calories is the amount of calories that comes from fat. in our diet, there contains fats in the food such as saturated fat, trans fat, monosaturated fat etc. when we consumed food, we cannot avoid consuming certain amount of food. such fat contains energy too, hence bringing about the calories coming from this fats. other form of energy that we can derived besides from fats are like carbohydrate (rice, noodle, pasta, bread), sugar, etc. when we purchase a food item, take a look at the nutrition label. it will usually write the total calories per serving which is the amount of energy we will get from one serving of that food (for example 100 kcal). then the label will also indicate that the food of which contains 20 kcal of fat calories. this means that of the 100 kcal of energy per serving, 20 kcal comes from fats.
to loss weight, one should reduce the consumption of fats. however, our body needs fats too (such as oil). i think it is more appropriate to identify the different types of fats in the food. avoid food with trans fats as those fat is very unhealthy and can even cause heart illnesses.
eat everything in moderation and exercise regularly should be the correct way to loss weight. excessive dieting will damage one's health and immune system.