Why It Works Tomato purée tempers ketchup’s sweetness, giving the sauce a more savory tomato base. Starting the shrimp in cool water and stopping at 170°F (77°C) yields evenly tender shrimp. A brief salt-and-baking-soda brine helps the shrimp cook up plumper and juicier. The distinction between what's called "shrimp cocktail" and what's called "ceviche" in Latin America is a blurry one. There’s no easy way to map it, but here’s a very cursory look: Starting with the most classic Peruvian ceviche, we find raw and cooked seafood in a flavorful lime-based marinade; moving up to Ecuador, we encounter all kinds of ceviche, some similar to the Peruvian ones, others diverging a bit by, say, mixing ketchup into the base—often when shrimp are involved; on to Colombia, and we confusingly find ceviche served in a ketchup-based cocktail sauce, while coctel comes in a thicker sauce that also contains mayo (check out  Kenji's description and recipe for the version from Cartagena ); head farther north, to…