Atkins and Keto are just marketing names for similar diet, but Keto takes it further. Every few years someone comes with a brilliant idea of repackaging and reselling the low carb diet. Atkins and Keto just stuck. I think it happens to high fat diets, because many people still believe that fat = bad, so the old diets fade in popularity over time and when they come back they are subversive and can be marketed as 'revolutionary.' This does not happen to veganism, because it turned into almost a cult, so they always have a core of cultists that keep it relevant and find new converts to replace the 80%+ who eventually begin eating animal products.
Paleo does not belong on that list. You can technically still eat all carbs you want on paleo, as long as they are not grains or processed food. Eliminating those makes it tougher to gorge carbs unless you consume a lot of fruit.
South beach does not belong on it either. It is high protein, low fat, and low on carbs that are not fiber (eventually).