Stories that are either connected to a certain place or internationally. You can easily have a character join or leave a story (as long as they are not too important for it) and they can still do other things when no events of that story happen at the moment. These are usually much longer than single-time events and can be of different scale, depending on the story.
Events, on the other hand, are a short time thing and usually involve, well, events happening. These can be something small like a birthday party for a character or a grand parade, opening ceremony or whatever else comes to mind.
If you want a character to join a story or event, just comment on it with the character, so that the story/event creator can add the character by editing the record. Of course, members can create both stories and events.