Yes those are all correct. There is a great deal of dialect variation (and even "idiolect" variation, I mean variation from person to person, even if they speak the same dialect)
"Carbonated water" sounds quite technical, like an scientific document about water types. It is the term used by wikipedia.
The consumption of carbonated water and non-alcohol carbonated beverages increased by 12.4% in the period 2012 to 2016.
"Sparkling water" sounds like advertising talk: not boring "still water" but exciting "sparkling water". So Perrier and so on are called "Sparkling water".
Bottled water? Certainly, sir. Would you like still or sparkling?
Soda water is a type of sparkling water that is used as a mixer with whiskey. It is usually highly carbonated and contains sodium bicarbonate, which gives it a particular flavour.
Individuals have their own words:
fizzy water, bubbly water, seltzer, pop, coke, ...