Emergent Narratives: One example of this is Club Penguin — genuinely. The players have a predefined space to explore, but this space never gets old because the players interact to form new stories. The places are the same for everyone, but they’ll come away with many different experiences.
Enacting Stories: An example of this type of story is Star Wars: Battlefront. The characters from the movies are present, and it’s set in the same worlds. Players feel as though they are part of the narrative, involved in battles between the Rebellion and the Empire.
Embedded Narrative: One example of an embedded narrative is in The Forest, an escape room style survival game. The game can be played without narrative, but in exploring the world the player happens upon clues that can be reconstructed in order to tell a story about what happened in the past on the island, which will eventually intersect with the main plot point.
Environmental Storytelling / Spatial Stories: Skyrim is a good example of this. Even outside the main plot, people can learn more about the world and its workings, and have a very compelling experience, simply by exploring the different cities and locations. In each location there are episodic pieces of the story.