Historically, ketchup was a class of condiments that all had a lot of umami like fish sauces and oyster sauces. Over time, different ketchups were invented, one of which was tomato ketchup. Its popularity grew, and the other ketchups were forgotten, so these days ketchup is synonymous with tomato ketchup.
What you've described is just called tomato sauce in my part of the world (Pacific Islands, Australia, New Zealand). So what we call tomato sauce, you call ketchup.
EDIT: I found this https://www.atlasobscura.com/articles/heinz-ketchup-australi...
Interesting. Do you have a different word for the tomato based sauce made from fresh or canned tomatoes often used on pizzas and pasta?
Tomato Sauce and Ketchup aren't quite the same thing here - ketchup is probably stronger and thicker, but they are used the same way.
Incidentally, the best tomato sauce is whatever magical sauce they use on the hot-dogs at A&P shows.
On the other hand, a pasta sauce would generally retain chunks of tomato, use less (or even no) vinegar, salt or sugar per unit volume; and it would be applied to non-greasy pasta in much larger volumes :)