The way I use the words (I'm not saying it's the only way), is that naturalism is when the dialogue or plot feels natural, and realism is where it might really be true. I think BB feels natural but it isn't realistic. Deadwood is the same I guess. The things that happen would not really happen, they are heightened and shaped, but they happen in a natural-feeling way. And to be honest real life often feels a bit like that to me.
When I posted a couple of weeks ago, before I'd finished watching season 2, I made a lot of predictions, and then I deleted them all before I posted. Now I'm sorry I did that, because my predictions were all wrong.
I said that I thought the main characters were protected, like the protagonists of an ancient comedy, from the worst. I used the phrase 'Deus Ex Machina' and predicted certain things would not happen. But in fact they happened, and the main writer in this interview for example, uses the phrase 'Lucifer ex Machina' to describe the final episode. Of course that's just as unrealistic as everything going right, but it can be just as uplifting.