that depends on your definition of equal. in terms of energy, yes. 100 calories from carbs or 100 calories from fat are the same to the body in terms of caloric value. the issue at hand where they are not equal is how the body accesses calories. your body gets energy from glycolysis and the chemical pathway occurs different depending on the molecule you're starting with. in addition to being converted to glucose, types of molecules will have additional effects on the body, such as alcohol's inebriation. you also need to be aware the body can only handle so much of a particular caloric source before that glucose is converted to fat for storage and different substances have different roles in the body's maintenance (that's why you need fat in your diet and can't live off protein alone). a calorie is just a measuring unit for the amount of energy needed to heat one gram of water one degree celsius. energy is energy in that regard so there is no difference; however, it's not about calories as much as it is the food source those calories are coming from and how they effect they body.