A basic installation question re: public_HTML directory ... am I misreading the install.txt file?

After uploading and extracting the drupal installation into my public_html folder, should I leave the unzipped contents in the newly created drupal folder, or should I move everything out of that folder and directly into the public_html directory?

That's what I take this following quote to mean (and it makes sense to me, since otherwise, to access the website people would have to direct their browser to www.example.com/drupal-7.15/), but I'm slightly confused by the wording "a directory within ... your public HTML directory." That makes it sound like it should be in a folder in public_html.

From the install.txt file:

This will create a new directory drupal-x.y/ containing all Drupal files and directories. Then, to move the contents of that directory into a directory within your web server's document root or your public HTML directory, continue with this command: mv drupal-x.y/* drupal-x.y/.htaccess /path/to/your/installation

Is this simply a case that I am misreading the text, and incorrectly applying the "into a directory within" to modify both "your web server's document root" and "your public HTML directory" when it should only be modifying the "document root" phrase?

If that is the case, to avoid the possibility of people misreading this direction, I suggest that that passage be revised by switching the order of those two phrases so "within" can't be misread to apply to both. I suggest something like:

This will create a new directory drupal-x.y/ containing all Drupal files and directories. Then, to move the contents of that directory into your public HTML directory or into a directory within your web server's document root, continue with this command: mv drupal-x.y/* drupal-x.y/.htaccess /path/to/your/installation