In drupal, it's possible to create a "build", also known as "install profile" or "distribution" that basically combines several modules and your settings for them. So the next time you setup the same exact site, you don't have to re-configure all the modules.
Does Joomla have a similar concept, and what is it called? Please reference documentation as well if possible.
The concept is very simple - you just need to get a clean installation, install all the extensions you want and configure them the way you need.
Then it is enough to copy the files and the database to a new location and change the settings in the configuration file (configuration.php). That is all.
It is a very simple process and can easily be automated with a simple php script. I once did an asp.net app which was deploying new installations of joomla within seconds.
You could try something like http://www.akeebabackup.com/
This allows you to take a snapshot of a site and export it anywhere.