They mean the same — "in spite of that" — and are interchangeable in almost every sentence. Nevertheless is the older and slightly commoner form; nonetheless is marginally lighter. Both are one word in modern English, and both take a comma when they open a sentence.
The core difference
None worth acting on. Both mean in spite of what was just said, both are formal-leaning, and no style guide separates them.
- The evidence was thin. Nevertheless, the case went to trial.
- The evidence was thin. Nonetheless, the case went to trial.
Swap them and nothing changes. If there is any tendency at all, nevertheless carries a fraction more weight, which is why it turns up more in legal and academic writing.
One word, not three
Both are written closed up. None the less as three words is an older British form that still appears occasionally and is not wrong, but it looks dated; never the less is simply an error.
Punctuation
Opening a sentence, both take a comma: Nonetheless, the deadline stands. Joining two independent clauses in one sentence, they need a semicolon before and a comma after: The deadline was tight; nevertheless, the team delivered. A comma on its own there is a splice.
The plainer alternatives
Both are long words for a short idea, and in most prose one of these reads better: still, even so, all the same, but. "The evidence was thin. Even so, the case went to trial" says the same thing with less ceremony.
Frequently asked questions
Is there any difference between nonetheless and nevertheless?
Effectively none. Both mean "in spite of that" and are interchangeable; nevertheless is slightly commoner and marginally weightier.
Is "none the less" as three words correct?
It is an older British form and not an error, but it looks dated. Nonetheless closed up is standard.
How are they punctuated mid-sentence?
A semicolon before and a comma after when joining two independent clauses: "The deadline was tight; nevertheless, the team delivered."