The point here is to keep a firm grip on the difference between relative and absolute URLs (relative and absolute paths are another matter altogether). With URLs, a leading / means "the root of the webspace" where the web server starts when it looks for its files. Omitting the / means "relative", relative that is to the .php script (or the .html file) being run at the moment. In our case, it's the index.php being run, whether the root-level index.php for front-end or the /manager/index.php for the Manager.
MODx offers two settings, site_url and base_url. The site_url setting will give the full first part of the URL for the site, such as
http://sottwell.sottwell.modxcloud.com/ (note the trailing slash is included). The base_url will usually just be the leading / to indicate that the base of the site is the web root. If the installation is in a subdirectory (and not an actual virtual host, where the web server takes care of the root location issue) it might look like this /revodev/ - it shows the absolute URL starting at the web root, again including the trailing slash.
[ed. note: sottwell last edited this post 13 years, 10 months ago.]