Different types of Calories?

That's not true at all. You can, for example, have a 1200 calorie a day diet but get all of your calories from mars bars and doughnuts and still lose weight. What you would also lose is the benefit of the minerals and vitamins that would otherwise be contained in 1200 calories of a protein/fat-based diet. Your insides would become covered in fat but you would still continue to lose weight in general. You would also not feel as full because 1200 cals of mars bars isn't a lot of food so you would end up eating more.

Sugar (carbs) affect your body differently to fat and protein, in the way that they affect liver function and insulin production, but a calorie will always be just a calorie.

I have heard about calories from carbs or sugars are worse for you. Someone mentioned that one calorie from carbs = 5 normal calories? Has anyone else heard of this?

It depends on your goals. If you are only interested in losing weight, then for the most part, a calorie is a calorie. If you're trying to go from 15% BF to 5% BF, then it gets a lot more complicated. Insulin responds differently to different types of calories, but it really depends on your goals to determine if it's worth getting that deep into the science.