Foods labelled no added sugar still contain sugar - eg fruit juice. In some cases the food may take the word sugar literally and so contain honey, etc. Which is ridiculous as that is sugar.
Sugar free is often misused, and may mean no added sugar although that is changing. It should mean no sugar at all, including no naturally occurring sugar.
Unsweetened, again can contain natural sugar.
But the key measure is carbs, in the USA net carbs (ie minus the fibre), in the UK the carb count does not include fibre. Our bodies convert carbs to sugars.