In everyday talk the sweet-sour ketchup served with fries; on cans it can also mean unsweetened concentrated tomato paste. Chinese cooks use it for the glossy red sweet-and-sour sauce on fried pork and fish.
番茄酱 can refer to both ketchup (the sweet condiment) and tomato paste/sauce used in cooking. In mainland China, 番茄 is the standard word for tomato; in Taiwan, 蕃茄 (with the grass radical) is also seen.