What are the categories you're saying can't be distinguished between? As I read you, it sounds like you have one called "trad" and one called "narrative". The 'trad' label puts in my mind the six cultures of play idea; you also say it is "like early D&D", but narrative is not one of those (story games is). You also don't want the GNS definition of narrative.
Maybe it is just that I'm late to the discussion, but I think the disconnect you and
@Micah Sweet have may just be about unstated definitions.
When I say there is a hard boundary, I mean: there are some games (which
@Micah Sweet and I enjoy) in which the DM takes authorial control of the world and the players control only their characters. Any mechanic which gives the players authorial control is incompatible with this, definitionally.
Based on that, we have two, binary types of games: "players have nonzero authorial control" games" and "players have no authorial control" games, right? That's a clear division. In my posts I have in mind "more authorial control = narrative", so I'm happy labeling these as "narrative" and "trad" games, respectively. Maybe that doesn't map perfectly, although I'm curious what games you'd call narrative where the DM retains all the authorial control. And cases where there is a hint of narrative control (especially limited in scope, like only prior to play) we may want to say more about.
But i think those details are details which don't contradict the core division.