There are literally thousands of diets. But they all differ in a few fundamental principles:

There are diets, which

• just reduce the food intake. You certainly know the infamous reduction
  diet or even starvation diet.
• handle it a little bit more intelligent and reduce the calorie intake. You
  know you found one of these if you have to count calories. A variant of
  these diets is the Weight Watcher diet where you count points which are
  calculated from calories, fat and fibre that food has per every gram.
• reduce the calorie absorption or the ability to store fat in the fat cells by
  combining food in a special way. Among these diets are the Hay diet, the
  method of Montignac or the Atkins diet.
• use food that boosts the metabolism and the ability to burn fat. Those
  diets are sometimes called "Fat Burner Diets". But be careful: Some diets
  called "Fat Burner Diets" barely care about food, but rely on drugs and
  pills.
• don't care about food, but rely solely on drugs and pills. Those diets are
  often called "Formula Diets". Some are even named "Formula Diet" -
  eventually with an addition.

In general most diets are combinations of the before mentioned models - intentionally or not. For example many recipes of the method of Montignac are high in vitamins. And its proven that vitamin C is a very effective fat burner. Another example are the well known "Slim Fast" products. They are counted among formula diets but offer also a menu plan.