In Australia and New Zealand, "soft drink" or "fizzy drink" is typically used. In South African English, "cool drink" is any soft drink. In other languages, various names are used: descriptive names as "non-alcoholic beverages", equivalents of "soda water", or generalized prototypical names.
The British version is called Diet Coke too. Coke Light is the continental European version, which you sometimes see in small shops and cafe's as I guess they can import it more cheaply than buy the local product. I imagine both are different than American Diet Coke.