The PATH is the path in the server's filesystem, beginning at the server file root. The base_url is the web server's URL, beginning at the web root. So for a PATH, / means the root of the server file system. For a URL, / means the web server's web root.
In your case, your hosting is putting everyone's files into /home/www/domain.com/ directories on the server. All of your files are in the /home/www/puschpull.org/ directory, and the web server uses your www directory as its web root (in the case of the web root / means YOUR www directory). Other servers may use public_html or htdocs as the web root directory; using www is common but in this case it's confusing you because they also use a directory named www to contain all of their customer's individual website directories.
You can use site_url to get the whole URL domain and all.
[[++url_scheme]][[++http_host]][[++base_url]]
is the same as
[ed. note: sottwell last edited this post 12 years, 2 months ago.]