Okay, that's a pretty clear example. By the definitions advanced here, SotC would be a roleplaying game if you added the words "You cannot invoke Aspects on anything but yourself" to the book. That way Aspects dealing with terrain are invoked by the GM based on your actions, rather than directly. Instead of saying "I light the stack of oily rags on fire, invoking "On Fire" as an Aspect", you'd say "I like the stacks of oily rags on fire," and then the GM would say "I'm gonna rule that invokes "On Fire" as an Aspect."
Or if you want to be stricter, disallow invoking Aspects on everything, period. That even eliminates using your own Aspects as feats or bonuses, meaning a person who's known as Sneaky can't get extra bonuses for their Stealth roll, but that's not that huge a deal.
So does that tell us anything useful? It doesn't seem like these definitions deal with hugely different types of play if a sentence of house rules can switch it from a storytelling game to a roleplaying game. It seems mostly to deal with whether or not the player can narrate stuff other than what their PC does, and then all that stuff just gets handed over to the GM to run for the player. So Aspects would give your PC a bonus when the GM said they did, instead of when you say, but there's not much else changed at all.
