As far as ketchup versus catsup….it Doesn’t matter they’re both misspellings. The original Chinese word is koechiap. In the 1600s the English term was usually spelled catchu and then it evolved into catsup (1680s) and ketchup (1711).
The term was originally a catchall for all kinds of vinegared and/or fermented sauces with a cookbook in 1817 listing one recipe for “ketchup” and 72 recipes for “catsup” Including variations with walnut, oyster, anchovy, herring, squid, cockle, mussle, cucumber AND tomato as the individual stars. According to Jonathan Townsend (a Youtube Channel on colonial cooking as well as manufacturing that I enjoy), mushroom ketchup was one of the most prevalent sauces during colonial era America and was used in place of where modern cooks would use Worcestershire sauce, soy sauce and/or an Asian fish sauce. Chambers's Encyclopaedia (1870) listed mushroom, walnut, and tomato ketchup as "the three most esteemed kinds” of ketchup. It wasn’t until Heinz created its magnificent version (and I only purposefully buy Heinz or Spicy Whataburger ketchup) that the tomato version became the ONLY kind used in America.