Unsweetened is a subclass of "zero/no sugar". No sugar added is a completely separate thing.
No sugar added does not mean the product doesn't contain sugar or that it's not sweet. It only means there was no extra sugar added during the preparation. A "no sugar added" fruit juice, jam or even ketchup is still going to be sweet.
Something like pure maple suryp qualifies as no sugar added despite being 99% sugar.