This is something I arrived at because I wanted a division into just two categories, payload cards and cycling cards.
What you're calling "cycling" here is a concept that I call "deck control" -- there are two concepts of payload and deck control and payload is defined as everything that isn't deck control. The intuitive definitions of them go like this:
Deck control is what you do that enables you to play other cards.
Payload is what you do that helps you win the game.
There are more rigorous definitions that I have, which are defined in terms that the game defines -- they hold up to scrutiny, but as you've probably noticed, they aren't exactly simple. I can talk about them in more detail if you're interested, but the high-level stuff is in these
two videos that I currently have drafts of, and plan to use in my video tutorial series in place of some stuff that's currently there. These videos use "cycling" in the same way that the podcast episode did, so obviously that will have to change before they are published.
So velocity, as I guess I'll call it in the rest of this post, is part of deck control, but there are other components to deck control besides cycling. Deck control is something that has a real definition and velocity is more of an abstract goal that you have, they're different types of terms for different purposes, but I've had a lot of success with people understanding deck control and how it influences the way they build and play their deck.
For example, to me Throne Room is a card that acts as cycling or payload, depending on what you double. And perhaps you can argue that according to the definition it should just be classified as cycling, because it's playing cards more often, but I don't think that captures the core essence of "cards that let you play good stuff more often + cards that give you stuff".
So Throne Room is a card that has lots of different modes, depending on what you double. You can use it as spamming if you want an effective extra copy of the card you want to play a lot of. It is a village, and some types of draw need the support of a village, so in that sense Throne Room can serve as draw in some cases, which is one part of velocity. It can be payload if you double a payload card, or can be multiple of these things at once (let's say you double a card like Market that has both deck control and payload components). Throne Room is pretty good because it can do all of these things for you, depending on what you need at the time.