Just to clarify. When you say cast, you mean the characters in the play and not the actors playing the characters?
So, you have the cast (as in the characters in the play) and the setting. But, you don't have any plot yet. And, typically, cast definitions are pretty sparse - Name (so and so's uncle), Name (so and so's wife) etc. So, no, not really at that point. But, once you start defining those characters in terms of conflict - giving them factions and motivations - then yes, I would call that a story.
At least, that's how I would define it.
Bob - a fighter. (not a story)
Bob - a fighter in Waterdeep (still not a story)
Bob - a fighter in Waterdeep searching for the Macguffin of Whatever in the Undermountain and will approach the party in order to try to hire them - that's pretty close to a story.
One might think about this from AW
A grotesque is a person—remember fundamentally a person, human, not a monster—whose humanity has been nevertheless somehow crippled. Choose which kind of grotesque:
Cannibal (impulse: craves satiety and plenty)
Mutant (impulse: craves restitution, recompense)
Pain addict (impulse: craves pain, its own or others’)
Disease vector (impulse: craves contact, intimate and/or anonymous)
Mindfucker (impulse: craves mastery)
Perversion of birth (impulse: craves overthrow, chaos, the ruin of all)
Threat moves for grotesques:
Push reading a person.
Display the nature of the world it inhabits.
Display the contents of its heart.
Attack someone from behind or otherwise by stealth.
Attack someone face-on, but without threat or warning.
Insult, affront, offend or provoke someone.
Offer something to someone, or do something for someone, withstrings attached.
Put it in someone’s path, part of someone’s day or life.
Threaten someone, directly or else by implication.
Steal something from someone.
Seize and hold someone.
Ruin something. Befoul, rot, desecrate, corrupt, adulter it.
For instance, Monk is a grotesque: pain addict, so his impulse is to seekpain. Maybe the move I choose for him just now is attack someone frombehind: “Damson, someone steps up behind you in the line for showers and loops a wire around your throat. What do you do?” Dog Head is a member of some brutes: hunting pack, so his impulse is to victimize someone who stands out. Maybe I just choose to announce off-screen badness:“ Marie, when you see Isle that morning her face is a mess. Somebody cut her cheek open with a heated knife. She won’t say who.” The rag-waste is a landscape: breeding pit, so its impulse is to generate badness. Maybe I have it disgorge something: “Keeler, you were out scavenging yesterday? Cool. You wake up before morning, there are these weird bugs all through your room. They’re about this big, black and red, a little like tiny crayfish. They’re in all your crap, your food, your clothing, your bed, which is what woke you up…”
I share (what I take to be) your sense that setting and cast, even with motives and a job to do, may not yet count as a story. As to what might count as story, one has to add plot but construction of plot is not one-sided. In most modes of play GM is looking after some threads while the players look after others -- the story is what they produce between them. To extend your example, the fighter approaches the party and they turn her down and do something else, so the story for that group unfolds in a different direction.
Perhaps narrativism (which I sometimes now reflect on as 'dramatism') is not particularly well distinguished from sandbox by GM being an author of story. Other differences could include management of scene, temporality and continuity, consciousness of authorship, the proper subjects and focus of play, how and when authorship is assigned and triggered, use of meta-mechanics... not as a matter of presence or absence but of emphasis or priority.
