@LeviKornelsen maybe mechanics that incentivize story creating action.
I'm thinking of stuff like a Cortex game that uses values as a die set. If you do stuff that narratively is based on a particular value you get an extra die so players are encouraged to drive their actions based on beliefs which, over time, creates a story about their beliefs and it's evolutions.
@LeviKornelsen I think the heavily constrained mechanical arc of My Life With Master doesn't quite sit in category 3.
Games like Montsigeur, Rosenstrasse are also, I think, a bit outside your categories: the "plot" is defined but the "story" comes from choices within it.
@LeviKornelsen I suppose so, but then a few things could cross boundaries.
I've got Story Points (5 XP for a backstory element, which does a current thing), which counts for 8, 5, 3, and possibly 6 (since the 'current thing' brings in a henchman, who can become a PC later).