Each soft drink has the same volume... i.e. 375mL However, they each have a different mass... weigh each one if you want!
Density is a measure of mass in volume... i.e. how much stuff is packed into a given space.
Regular soda drink contains a large amount of sugar, making it more dense than the diet soda drink. The diet soda floats above the regular soda because it is less dense. Think about your teeth!
The diet soda most likely contains a small amount artificial sweetener called Aspartame. Aspartame is 200 times more sweet than sugar so you dont need much.
Your diet does influence your health. Whether you eat entirely natural foods or those with partly artificial ingredients, food technologists has played a part in developing those products. In fact, nearly every food you eat has been selectively bred over thousands of years.