What is the difference between ketchup and cocktail sauce?

No, not in the actual condiment. The two versions are merely alternate Westernized spellings of the original fish-based Chinese sauce that ketchup hails from. This proto-ketchup became popular among Western traders in the late 17th century.

As it gained traction in Europe, the sauce went through many incarnations (including a walnut-based version) before settling on the tomato goop we know and love. That’s why it says “tomato ketchup” on some bottles—it seems redundant today, but that’s only because no one goes around asking for walnut ketchup anymore.

“Ketchup” is the more popular spelling, and it became so in the mid to late 20th century. Heinz was an early “ketchup” adopter, and other big brands switched over as it gained more market share. But either spelling is technically acceptable—for example, the USDA exclusively uses “catsup.”