Every time I get to Southern Illinois, there's a small diner in Cairo I like to go to that serves ONLY RC products.
That's the only place I've ever been that doens't serve Coke or Pepsi.
As for Pepsi, Coke, and RC all being coke, no. They're all cola. Only Coke is coke.
Coke used to have a trademark on the word Cola, as well, but they left Pepsi use it for years when Coke was the only big national soda. But when Pepsi started competing with them, Coke turned around and sued over the use of the word Cola, saying it was a trademark infringement. Pepsi countered with the argument that Coke had allowed the trademark to expire through benign neglect. Pepsi won. Moral of the story? You have to protect your intellectual property. If you don't, you'll lose it.