What do the claims "sugar free" and "no sugar added" mean on a food label?

The nutrient content claim "sugar free" on a food label means that the serving of food contains an insignificant amount of sugar (less than 0.5 g per serving).

The claim "no added sugars" or "no sugar added" is allowed if no sugar or sugar-containing ingredient (such as jam, jellies, or concentrated fruit juice) is added during processing. This claim is only to be used on foods that substitute for foods that normally contain sugars. Also, unless the food meets the criteria for a "low calorie" (i.e., 40 calories or less per serving) or "calorie reduced" (i.e., 25% reduction in calories) claim, it must say it is "not a low-calorie food" or "not a reduced-calorie" food.