“Nonetheless” and “nevertheless” mean have the same meaning, but the usage of these words are different. Nonetheless, it is less frequently used compared to “nevertheless” this is because many people prefer to use the word “nevertheless.” The consensus says “nevertheless” sounds better.
Linguistic historians will also note that “nevertheless” appeared in English usage much earlier than “nonetheless” which appeared centuries later.
.“Nevertheless” is used more frequently in the active voice, when the subject of the sentence acts on the verb. However, “nonetheless” should be applied to something which is measurable quantifiable.