A Basic Git Question About File Tracking

I've been reading the Pro Git book. I'm having trouble really understanding the concept of file tracking. Here's where my confusion starts.

The Pro Git book says "Untracked basically means that Git sees a file you didn’t have in the previous snapshot (commit)".

Is this right? I can easily think of a counter example. Let's say you put a new file in the working directory of a Git repo. Then you "git add" it. At this point, the file hasn't been in any commit. Yet, 'git status' doesn't show the file as being untracked. Should that statement be "Untracked basically means that Git sees a file you didn’t have in the previous snapshot (commit) or a file that hasn't been staged."?

One additional confusing thing is that "git add" apparently both starts tracking a file and puts it in the index the first time a file is added. Thereafter, "git add" only puts the file in the index. One of my research projects is to understand what goes on internally when a file is tracked.

Jon Forrest