When I was a child, the common terms for soft drink were "cold drink" and "coke".
On a hot day: "I'm going to the store. Do you want a cold drink?"
In a casual restaurant:
"I'd like a burger and a coke please."
"We have Pepsi (or Coca-Cola; never both). Is that all right?"
"Same thing*."
* I'm sure that will appall marketing types at both Coke and Pepsi, but it's the truth.
No one would ever say "I'd like a Pepsi coke (or Coke coke), please."