Alternative term for a story within a story

I am trying to find the term for a story that exists on the side, in the background, or margin of another story but may or may not be related to it. The only examples I can think of are in comics or TV.

1. Cartoons by Sergio Aragonés that appeared within the margins of Mad Magazine and are referenced by Wikipedia as "Marginals".
2. The ongoing saga of Itchy and Scratchy that exists within each Simpson's Episode, I guess could be called a "Running Gag".
3. Another one is the Thomson & Thompson "side story" that usually appear in Tintin Adventures, although those are generally still related to the main plot.
4. The best and most precise example of what I am trying to term is the Belgian comic Leonardo, which have a cat and mouse character that engage in their own story in each panel completely independent of the main story.

I am looking for an alternative term to Marginal, Side Story, or Running gag if one exists that could define all of these variants.

If anyone has better examples in writing or other media, I would appreciate it.

Solution 1:

You should check parallel narrative:

https://www.theguardian.com/books/2014/jul/02/philip-hensher-top-10-parallel-narratives-mrs-gaskell-david-mitchell

Example usage in academia:

Parallel Narrative Structure in Paul Harding’s Tinkers

Some more from Wikipedia (interestingly this is a result thrown on search of parallel narrative):

Nonlinear narrative, disjointed narrative or disrupted narrative is a narrative technique, sometimes used in literature, film, hypertext websites and other narratives, where events are portrayed, for example out of chronological order, or in other ways where the narrative does not follow the direct causality pattern of the events featured, such as parallel distinctive plot lines, dream immersions or narrating another story inside the main plot-line.