This is a somewhat basic question but I cannot find an answer yet. I was under the impression that "no" should be a synonym of "without" but it seems not to be (at least on the synonym sites that come up on Google). The definition of synonym does state that a synonym is a word that is nearly the same as another word.
I can say that the cup of coffee is without sugar or that it has no sugar. They both mean the same thing - the critical words are "no" and "without". The more detail someone can provide the better and I have no problem with being corrected if I am in error.
Update: this also lends to the idea that they are synonymous: https://forum.wordreference.com/threads/coffee-without-sugar-with-no-sugar.1535936/