There are actually three SOFT DRINK synonyms in America:
1. SODA in New England and Northeast
2. POP in the midwest extending through to the Pacific Northwest
3. COKE in the American South.
Two out of three of these words makes sense given the histories of soft drinks in their regions. The word SODA was probably more entrenched in the vocabulary of the Northeast by the time that Coca-Cola emerged in the late 19th-Century. The South say COKE, of course, is where Coca-Cola originates. Its ubiquity may very easily have resulted in this particular brand being synonymous with soft drinks of all kind. (Much like “Band-Aid” has become synonymous with small bandages).
Which leaves the onomatopoeic POP native to dialects of the Mid- and Northwest, so named, apparently, because of the sound made when removing a cork from a carbonated beverage.
The British call soft drink as FIZZY DRINK although they also call it by its brand names, such as Coke, Fanta, Sprite, Dr. Pepper, 7Up, etc.