Difference between nevertheless and nonetheless

I am never quite sure whether to use nevertheless or nonetheless; they seem almost synonymous to me, but I think I might be missing a subtle distinction. Is there a difference, and if so, how do I determine which is right in different circumstances?

I am specifically thinking of sentences such as these:

• I am busy Saturday; nevertheless I will come to your party anyway.
• I am busy Saturday; nonetheless I will come to your party anyway.

There is a question here that deals with a specific idiomatic usage, but I was thinking of the general type of usage, as given in the party example above.

Solution 1:

The regular MW dictionary entry for nonetheless actually just says "nevertheless," and I'm not personally familiar with a situation when you could justifiably use one but not the other.

According to merriam-webster.com's Learner's Dictionary, they have the same definition as well:

in spite of what has just been said

…although nonetheless is marked as somewhat formal, while nevertheless is not.

Solution 2:

Nonetheless is used when talking about an amount of something.

He really botched it tonight. I love him nonetheless.

Here we are saying that the amount I love him has not been diminished from the level I loved him prior to his having botched it.

Nevertheless should be used when talking about doing something despite the facts.

It could be dangerous. Nevertheless, I've got to try.

Here we are saying that I will try despite the fact that it could be dangerous.

Note though that quite often interchanging the words results in a sentence with a different nuance of meaning but the same overall outcome.

Switching to nevertheless in my first example changes the meaning from I don't love him any less to I love him despite the facts - very similar but not quite the same.

And this is why interchanging them works so often. Because usually when saying that the amount that I do something has not diminished in any way it is because something has occurred that had the possibility of diminishing it and in not diminishing the amount I have essentially done that despite the facts.