Ketchup vs. Catsup

What is the difference between ketchup and catsup?

How come they call it “ketchup” sometimes and “catsup” other times?

Same word. From Maylay kechap- brine, sauce from Chinese ketsiap.

And if you run into someone who claims that ketchup is a “dumbed down” spelling of catsup, aim them at the OED where a couple of ke- variants appear before any ca- variants (although not by enough years to justify giving either priority).