Basically, there is no difference. Catsup and ketchup are alternative spellings of the same word for a tomato-based condiment.
The American Heritage Dictionary provides the following fascinating word history:
The word ketchup exemplifies the types of modifications that can take place in borrowing—both of words and substances. The source of our word ketchup may be the Malay word kechap, possibly taken into Malay from the Cantonese dialect of Chinese. Kechap, like ketchup, was a sauce, but one without tomatoes; rather, it contained fish brine, herbs, and spices. Sailors seem to have brought the sauce to Europe, where it was made with locally available ingredients such as the juice of mushrooms or walnuts. At some unknown point, when the juice of tomatoes was first used, ketchup as we know it was born. But it is important to realize that in the 18th and 19th centuries ketchup was a generic term for sauces whose only common ingredient was vinegar. The word is first recorded in English in 1690 in the form catchup, in 1711 in the form ketchup, and in 1730 in the form catsup. All three spelling variants of this foreign borrowing remain current
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What is the difference between Ketchup and Catsup
