So people in the south just call all sodas Coke?
Yes.
"What do ya'll want to drink?"
"A coke."
"What kind?"
"Pepsi."
See, now what if the conversation went like this:
"What do ya'll want to drink?"
"A coke."
"What kind?"
"Sprite."
If I witnessed such dialogue, I would either smack somebody or collapse in a heap of bewilderment.
As far as I know (like I said, I grew up in a part of the South that calls it soda always), coke only applies to sodas that look like coke. I don't think anyone calls mountain dew or sprite a coke.