It's not that there aren't different kinds of rules. It's that there's no real need for a distinction.
In game design there is. Its a difference that matters for quite a lot, actually, as a games design should be placing the bulk of the complexity within the Rules.
Content shouldn't be adding additional complexity that isn't a part of the Rules, and where it inevitably must should be kept minimal and worthwhile.
Something like a Class having a unique core mechanic of its own, for example, makes sense in this regard. If a Warrior has their Mighty Deed, its a worthwhile complexity thats being added within the Content of the game, and it isn't egregious that its there.
Whereas while something like the 5e Druid requiring a wholly separate book from the PHB to play violates that criteria; while one can debate the worthwhileness of Generic vs Specific Statblocks from a complexity standpoint, one can't really argue that much of the classes required material is in a book thats not meant for Players is a good thing.
But beyond that, making the distinction is also just a good design philosophy, especially in translating an entire Game, Rules and Content together, into something teachable.
Rules can be taught and internalized, and then built upon by Content, keeping the learning curve nice and smooth.
Additional Rules introduced by Content, if kept efficient (ie, minimal and worthwhile), won't violate that learning curve. The Mighty Deed in DCC for example is a pretty simple Rule. As part of your roll, roll a die of such and such size. If you roll at least a 3, you gain the use of a Mighty Deed, which might be improvised or might correlate to some result on a Deed table.
Ezpz.
Whereas in the Druid, one not only has to learn the already pretty complex Full Caster framework, but also has to become accomodated with the Monster Manual and learn the ins and outs of the various beasts available to them, which in turn must be located and cross checked with the Druid rules to ensure they can be used.
Thats a lot and isn't terribly worthwhile compared to a (good) Generic statblock system, or to just printing the eligible Beasts in the PHB for ease of reference.
I don't know FATAL, but I'm pretty confident that if I wanted to come up with some different rule or in some cases no rule for something, I could do it
FATAL is where the "roll for anal circumference" meme comes from. Its not so much that you couldn't, mind, but that you wouldn't want to. Because you'd quickly realize you don't want to play the game at all upon touching the book. (And god help us if you do want to play for any reason other than sheer academic masochism)
My point is that even in D&D you can do away with 1d20+ modifiers and still play the game. We can flip a quarter to see who wins, or if we want to get more complex, each side flips a number of quarters equal to their bonuses and the most heads wins.
But at that point you are genuinely not playing DND.
Admittedly, I haven't thought much on the idea of not using the core mechanic, but still using everything else in the Game, but with how much relies on the Core mechanic, Im not certain how well that would work out, if at all.
Either way, you'd ultimately still be replacing the Core mechanic, not just dropping it outright and using nothing in its place.
But even if you did, at that point you're basically doing some sort of weird FKR-DND frankenstein monster. And even then, you're still technically replacing the resolution mechanic with common sense.