How... I'm not sure I see the point in trying to draw a distinction between these two things (a distinction that you admit is lost on a lot of people). Both are role-playing, in the context of an RPG. Performing an act in a fictional space is the same as telling a story about the performance of that act.
(Ouch, now my head hurts)
The distinction between role-playing and storytelling is well known outside the hobby. Inside the hobby there are several people using an incorrect theory that is confusing them into believing the two are the same. Storytelling isn't role-playing and you can't do both at the same time. It's functionally impossible.
To be clear, doing something is not necessarily equivalent to portraying something. It's the difference between normal existence and theatre acting. In your response, I believe you are confusing 1. action occurring in a modeled space with 2. collaborative storytelling. Just because the action is being modeled on a gameboard you cannot see does not make unreal. Yes, there is narrative discourse going on. Yes, elements of it are imagined, are ideas, which fall under one definition of "fiction". But no, there is no "fictional narration" going on.
I get this tweaks people's brains, but for decades most players understood this quite intuitively. In the same way that the winners of 4E's combat system do not win because they "tell a better story", role-playing is the real success of playing a role in an actual reality. That the dice rolling and rule following created a model of reality, which is attempting to recreate (emulate?) an imagined idea (the world), it does not mean the model isn't real because the emulated fiction isn't real. This true in the same way playing a boardgame is real even though its' rules are trying to model a fictive reality.
I mean, really, if it was all just a bunch of collaborative storytelling, no dice rolls or numerical descriptions would ever be needed. The quality of the story would rule all.
If the DM and player agree that the event happens, then it de facto relates to the gameworld. "Relation to the gameworld" established through participant consent.
Participant consent does not mean the action is role-playing. In Skill Challenges, the players are taking authority over the reality of the world, not their merely their characters/roles. In other words, they are telling a story and not role-playing their characters. To take it one step farther, playing God is not role-playing or we will quickly find ourselves in the black hole of every game qualifying as a role-playing game.
Which doesn't change the fact that the events occurring inside the shared imaginative space of a role-playing game are best understood as being story-like ie, the actions of fictional, person-like characters in an imaginary, life-life place.
Where you say story-like I think you should say life-like. This modeled space is a real construction just like a boardgame representing things in life.
Story is the relation of events real or imagined. You cannot "take action" in a story because the storyteller isn't a character. He's relating the actions of the characters. In a role-playing game you are absolutely taking action. In the exact same way a DDM player is taking action.
Seeing as the 'external reality' in question is a fictional construct being sustained by mutual consent and is often, in practical situations, rather fluid, I'd say this isn't a particularly helpful assertion.
That's like saying, playing Doctor Lucky and making house rules up as you go beyond the elements the published rules focuson, then you're telling a story. Almost all games are simulating something. Sports are probably an exception, but most boardgames and cardgames likely count. The reality in each is as solid as the rules create.
Unless, of course, the DM says otherwise. Are you really saying that anytime a DM gives (limited, localized) narrative rights to a player, it ceases to be a role-playing game?
No, the overall game would be a hybrid between role-playing and storytelling. Also, I'm not here to talk about game identity. I'm talking about actions real people take within a game. You cannot do more than your character can without stepping outside your role (i.e. stopping the role-playing your character). This seems immediately obvious to me. Once you start dictating reality, your in God Mode (authoring a story).
OK, that's exactly what you're saying. Where's the threshold? If the DM allows a player to shop for items without actually playing out the purchases, essentially letting the player narrate the event, does the game stop being an RPG?
No, this is not a player narrating an event. It's an abstraction of role-playing, but if done too often and too broadly it certainly may no longer qualify as role-play. That said, the player couldn't purchase the items at those prices if in he were in area with different prices. Or if his PC was nowhere near a seller of those items. To allow otherwise would be to metagame or cheat: to do something your character cannot functionally do in this case.
To clarify the point on being too broad or abstract:
Just as you can role-play being a stock trader by playing the market with an imaginary stock portfolio, you can begin role-playing so broadly as to no longer qualify as "role-playing a stockbroker". Instead, you're just pretending you have money in stocks and seeing how much they went up or down. The degree of modeling is simply not enough for most people to qualify it as role-play. The same could be said of fantasy football being the role-playing of a team owner. It probably isn't at all as very, very little of the role is modeled. Of course, in neither case can you "just say" you won without leaving all of reality behind and simply telling a story.
If you actually go for the walk, you're existing. If, instead, you create a representation of the dog-walk, say in conversation or text, then your storytelling. Extending this, seeing as gamers are never actually doing the things they're characters are doing, they are never existing as their characters, and can be said, in the interest of brevity, to be telling stories about them.
You're right in the first and second sentences and wrong in the third. Role-players
are doing the things their characters are doing. Not to belabor the point, but just as a flight simulator doesn't mean you are actually flying, it does mean you are actually the one doing the flying that is simulated. In a fantasy RPG, the players honestly and truly are not their characters, but they are taking on their roles. The fantasy world simulator allows this to be real as much as the simulator is capable. It is as much a storytelling endeavor as using a flight simulator is so (i.e. not at all).
If there were no flight simulator or fantasy world simulator, you definitely could say the participants were just telling stories about flying or being in a fantasy world. But in order to not "just say this is so" we use the rules and make up house rules to cover the areas we want covered by our favorite RPGs games. Check any House Rules forum for more proof on how story doesn't come into play when rules don't cover a situation.
If the existence(s) in question are fictional, then yes, I equate trafficking in them w/storytelling.
You'll notice Pemerton above agreed that not all imaginings or the holdings of ideas (thoughts) is storytelling. It seems like you believe the opposite. All I can say is, no one outside of the Indie gaming community probably defines "story" in this way.
And how is that not storytelling, using the plainest, most theory-free definition of the word?
Here was my phrase you're referring to:
"I don't believe a DM/Referee ever gets to tell a story. He merely relates back to those playing what is happening in the world."
Yeah, I tossed this one in there thinking I'd catch someone trying to call me on it. Check my first response in this post. It's the difference between using narrative discourse to refer to the real modeling of imagined ideas (fiction) and the rhetorical mode called "fictional narrative".
heh heh

I know it's tough. The difference is in short:
Occasionally using narrative speech forms to talk about modeled fiction vs. collaboratively relating a fictional narrative.
I completely sympathize with folks who believe The BIG Model because of this confusion.
Monopoly isn't a storytelling game because the action in Monopoly isn't sufficiently story-like. RPG's are story-like because they deal with person-like characters acting in life-like imaginary spaces.
When you say, "the action in Monopoly isn't sufficiently story-like" I get confused. What kind of boardgames, cardgames, wargames, whatever-games would it take to show this is not collaborative storytelling even with a "story-like" enough game?
Now if these blind players were playing D&D, it most certainly would be a storytelling game.
So, is D&D Miniatures a storytelling game when played with the blind, but not the seeing?
And that kind of role-playing isn't what's going on in most D&D campaigns (well, at least in any of the ones I've seen, read or heard of).
As the activity is role-playing, it's educational. Not to say other activities are not educational. It's just in D&D the skills learned are rarely modeled well enough to aid in real life. Combat would seem the best modeled activity, but I doubt it will help anyone in a real fight. Learning how to face adversity, plan, and make decisions quickly are probably more likely learned skills in D&D.