As Lambie says, drinks are either carbonated or non-carbonated. I believe these are universal terms used in government or official communication.
In the US:
Carbonated soft drinks are collectively referred to as soda, pop, and in some parts of the country Coke (even for carbonated drinks that are not Coca-Cola). Non-carbonated drinks are referred to by name (fruit punch, lemonade, iced tea, etc.)
Regular water can be either bottled or tap (meaning from the faucet). Carbonated water can be called soda water, and still may be referred to that way when ordering mixed drinks, (e.g. a scotch and soda). These days, however, bottled carbonated water is usually sparkling water, or colloquially bubbly water. Fizzy water also works.
In some fancier restaurants, if you ask for bottled water you may need to specify whether you want sparkling or flat.
Recently there are some naturally carbonated drinks such as kombucha which would not be grouped in with soda, as that usually refers to sweet carbonated drinks like Coke. Because it doesn't really fit into any category, just call it by name, kombucha.
Side note: Historically "soft" drinks were those without alcohol. At a large social gathering, for example, there may be a "soft" punch for the children and adults who didn't drink, and a "hard" punch for the rest. These days when you say "soft drinks" people mostly think of soda, but, technically, it does include any flavored non-alcoholic beverage.