I suspect soft drink is a generic term used nationally. Everyone knows what it is, but don't necessarily use it when speaking.
While Coke may be used regionally, people can get really confused by it, so it rarely appears in written form unless the reference is actually to Coca-Cola. But then, most of the time, the menus will print Coca-Cola with the Coke logo.
As a side issue, Coca-Cola Co. gets really upset when people use "Coke" generically to refer to any soft drink. Trademarks are everything, so companies avoid getting their products classified as generic to the point where Coca-Cola Co. will send ringers into a restaurant and ask for a Coke. If they get anything else but Coke, out come the lawyers. This is why a server is taught to say, "How about a Pepsi?" or something similar if they don't actually have Coke products. It's to prevent being sued.
Just ask Kleenex how they feel about being generic.
Companies actually will spend millions of dollars on research to find a name that means absolutely nothing in every language on earth. That way, they can more easily avoid being labeled generic. For example, Esso discovered that there is no language that uses two X's together in a word. So came the name change from Esso to Exxon.
For those who are curious, I use the term, "soda".
