To supplement @The Raven's solid answer, I offer these:
1711, from Malay kichap, from Chinese (Amoy dialect) koechiap "brine of fish." Catsup (earlier catchup) is a failed attempt at Anglicization, still in use in U.S. Originally a fish sauce, early English recipes included among their ingredients mushrooms, walnuts, cucumbers, and oysters (Johnson, 1755, defines catsup as "A kind of pickle, made from mushrooms"). Modern form of the sauce began to emerge when U.S. seamen added tomatoes.
- An Ngram of catsup (blue line)
vs. ketchup (red line).
- And a quote from Jeffrey Steingarten's excellent The Man Who Ate Everything:
Where did ketchup get its start? The most popular theory is that the word itself defives from kôe-chiap or ké-tsiap in the Amoy dialect of China, where it meant the brine of pickled fish or shellfish. Some people prefer the Malaysian word ketchap (spelled ketjap by the Dutch), which may have come from the Chinese in the first place. In either case, sometime in the late seventeenth century, the name (and perhaps some samples and a recipe or two) arrived in England, where it first appeared in print as "catchup" in 1690 and then as "ketchup" in 1711, at least according to the Oxford English Dictionary. These exotic Asian names struck an evocative chord among the British, who quickly appropriated the names for their own pickled anchovies or oysters, long in popular use and probably descendants of the fishy, fermented Roman sauces, garum and liquamen.