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
I've been working for years as a JOOMLA developer. You can do anything with all the most known content management systems(CMS).
MVC is the pattern there too. You can develop your own components, if you need something special.
Furthermore, you do not need to focus on developing common tasks, such as user management, Facebook co-operation, e.t.c.
Why reinvent the wheel? Anything that has been build before, can be bought or even downloaded for free from the repositories. There are so many components out there.
As for appearance, there are 1000s ready made templates that you can get and speed up your development and lower your cost.