I grew up in California where it's usually called "soda," but I generally used (and still do use, when I don't think about it), a Southernism that I picked up from my mother, in which "coke" means "any carbonated soft drink, including Coca-Cola." In my family, a perfectly common and comprehensible conversation might be something like this:
"Would you like a coke?"
"Yes, thanks. Do you have any Seven-Up?"
Yeah, or while ordering, you say "I'll have a coke" and the server asks "What flavor" or "What kind". I picked that up when I was in college down South. I generally say "soda", but will occassionally lapse.