Your question does contain an accurate description of these features. But I think I can add some useful information.
appears to affect only the open tab and creates a new circuit for the site in that tab
This is exactly right, and it is really useful for a number of reasons. I use it if the site I am visiting asks me to solve a CAPTCHA and this often solves the problem. this question contains more reasons why we might want to use this feature. (I have pasted them below)
Some times we may have to change when a circuit is slow, or if it does not allow certain traffic on policy. To lose all tabs for this is a huge burden.
As for your comment on the Entry Guard, the behavior you noticed should be the same for New Identity as well. This is what Entry Guards are designed to do, see here in the Tor FAQ.
closes the browser and reopens it
Again, this is correct, the important thing to note is that as well as giving you a new circuit, it's discarding your application-level browser data. As stated in the FAQ.
Finally, I will include a link to the stem.torproject FAQ because it contains useful information on creating new circuits.
As it was requested by jtd, here is a link to more information on the "New Identity" feature and how it discards application-level browser data.