How would you explain the difference between a PHP Framework and a CMS (like Wordpress) to someone who is very technically savvy, mostly on hardware/networking, but does little
You can check out this slide to see the difference:
To put it in simple words:
A CMS provides you with a back-end (with a host of plugins and components) like Joomla, Drupal, WordPress, etc that allow you to manage front-end. Where as a frameworks doesn't.
A framework such as CodeIgniter, Kohana, CakePHP, Symfony, etc: provides you with ready-made classes and libraries BUT you have to use them and build your own site ie: Front-end and Back-end.