You have two different questions in this post.
Your main question (about the difference) is that files with "nb" in the name is a notebook. It reflects the same things that you have run interactively. So, for example, when you click on the "Play" arrow for a chunk, output of this chunk will be in this file. However, to get all the things you've mentioned (css, TOC, etc.) you need to knit the document.
Basically, "nb" file is a preview. Once you knit, all of the chunks will start from new R session, so the document you get at the end (without "nb" in the name) is reproducible.
As for the error you are seeing ("RStudio not running") -- I have no idea what that means, unfortunately.