CMS = Content Management System.
Brandon was being a bit lazy when he was talking about this. Because it's a long conversation. And it's a short podcast, after all. And I'm going to do the same because I don't have a ton of time to explain the difference among the two systems, all the history behind them and how we've got to this point etc. In fact, I'm going to be leaving a ton of information out of this comment.
The one best way to understand what the differences are is to give the Craft demo site a look over. Download it, install it and see what makes it tic. Or better yet, you could get your feet wet and build a small site with it. It's fun. If you get it, you'll really get it. If you don't, well, what can I say. It wasn't your thing.
Just to touch on it real quick, basically, WP and Craft evolved very differently. The paradigms were, and still are, very different. WP manages content, as well as many other things, differently. That's why allot of people don't consider it [WP] a CMS. That and because it started out as a blogging system. It has, however, evolved and can now manage content in a similar fashion to Craft (yes, similar, kind of but, definitely poorly executed. So many other things are just wrong, mind you.)
This with the help of an additional plugin like ACF (advanced custom fields dot com) (Magic Fields before it; almost) An after thought. It just wasn't built from the ground up to manage content the way Craft and some others do. Not from the start, anyway. And not without a plugin; or using something like short codes; nah that's just nasty code soup. Something like ACF. Or some other craziness like Visual Composer (I don't even want to go there. I'm starting to get sick; but not for me, for my clients.)
Craft doesn't use themes. And this is a good thing (at the level we're talking about.)
ExpressionEngine before it (partly thanks to Brandon's previous work) and a CMS like Drupal (many Drupal devs don't consider WP a "true" CMS either) are what many devs refer to when they talk about real or true content management systems. Note: I'm not implying that Craft and Drupal are the same, however. They're not. But, in regards to content management, they are more similar to each other than they each are similar to WP.)
Of course, everyone has their opinions and their own way of doing things and I could continue discussing this but, eventually it's going to sound like politics and me throwing fuel on some imaginary fire (flame war anyone?)
Anyway, it's just different and this in a good way. Take it for a spin. If you're into backend stuff, take a look at the plugin architecture (see their docs), build something. See how it goes for you. If you have any questions, hit us up in the Slack Channel (see community section.)