As with so many things, it depends.
When used in contrast to a hot alternative, cold simply means at or somewhat below room temperature. For example, the meat in a hot pastrami sandwich is heated on a skillet as part of its preparation and served hot, whereas a cold pastrami sandwich it is not.
Food is also cold if it is usually served heated, but has cooled off below the temperature where it is normally consumed. Thus, your lukewarm chicken noodle soup may still be warmer than the air, but you may still send it back to the kitchen as "cold."
If the temperature of a food were deliberately lowered as part of its preparation, with ice or refrigeration, it would be chilled. For example, you might have chilled wine served with your dinner and chilled fruit for dessert.
Sometimes, hot and cold distinguish between levels of preparation. A cold lunch would be one brought from home (aka sack lunch), or a box lunch of a sandwich or fruit, as opposed to a hot lunch which would be a heated, prepared meal. Schools may offer a choice of hot lunch or cold lunch, for example.
Ketchup is a condiment, and so would almost always be cold, but would probably not be chilled.
I should note that with beverages as opposed to food, cold does sometimes mean chilled, at least in American English. You'll advertisements for cold drinks, typically meaning chilled fruity or fizzy soft drinks. A cold beer is idiomatically one that has been chilled below cellar temperature (well below room temperature)— we would not order chilled beer in a bar without raising some eyebrows.
But there are certain drinks which are taken hot or chilled, and never at room temperature. Thus, cold coffee or cold cider is hot coffee or cider that has been allowed to cool off— not something you can typically order. To get the truly cold alternative, you order iced coffee or chilled cider.
Lastly, there is the expression Revenge is a dish best served cold, but cold here is a play on words, referring to cold-bloodedness (i.e. heartlessness or mercilessness).