I remember seeing a linguistic graph of the US showing how different regions referred to fizzy sweet drinks (here in Australia, that's 'soft drinks'). The predominant usage was 'soda', fair enough, I can see it. Then there was a fair area of 'pop', which sounds cute and archaic to my ears, but fair enough. The confusing one was a swathe of the US south where they're referred to as 'coke', regardless of the actual drink. I remember someone here on HN relating the story of being asked to get some coke, came back with Coke, and being told he got the wrong thing...
The Coca-Cola Company is based in Atlanta, in the South. It's where the drink has existed the longest. Still crazy, but maybe that gives some perspective.
And somehow that trademark is still not generic.
In the south, you almost always ARE getting a Coke product. Pretty much only at Taco Bell/KFC are you getting a Pepsi product.
The proper exchange is:
"I'll have a coke."
"Which kind would you like?"
I live in Atlanta. It's no weirder than Xerox to mean photocopier honestly once you've noticed.