I don't think I have ever heard people say "carbonated water" in any metropolitan area. In the school lab, school canteen and deep in the countryside - perhaps. In 2015, "sparkling or still" has become the universal norm. If you are drinking whiskey, then your "fizzy water" is called "soda water". Whiskey and soda, even in country pubs. I don't think anyone says "fizzy water" except when talking to small children.

....and just one extra distinction. Some sparkling water may be naturally effervescent, while 'carbonated water' is manufactured.

From what I hear other people in the U.S. say they and including myself mostly say carbonated water. You can really use any of those and people would understand what you are talking about.

You can say either 'fizzy water' or 'sparkling water'. 'Sparkling' sounds a bit fancier. 'Carbonated water' is a rather more practical/scientific term, so you'd be less likely use this when talking about drinks. And yes, 'still water' is the opposite of 'fizzy water'.