When I first began writing novels, an editor-friend told me my writing was too linear. I didn’t know exactly what that meant, but I had some ideas. Now, many years later, and after writing four novels, I have a much better grip on the differences.
As I understand it, all plots are linear, but the way they are structured can be linear or non-linear. In linear writing, the plot structure moves from point-A to point-B to point-C to point-D, and without flashbacks. The storyline tends to be more plot-driven than character-driven, meaning the main characters could be replaced by different characters without much, if any, changes to the story.
In non-linear writing, the plot structure can bounce around, maybe with flashbacks, dream sequences, and/or scene switches with point-of-view switches, as when a plot has multiple storyline progressions that jump back and forth. It may include foreshadowing, and will most likely have character memories, emotions, and personalities that affect the direction of the story. If the main characters were replaced with other characters, the story would go off in a different direction. You would have a different story altogether. The story tends to be more character-driven.
Also with non-linear writing, you might start out at the end, for instance at a funeral, and then go back to the beginning and tell the story of what happened, or in other words starting with point-D, then going to point-A, point-B, and point-C. In other stories, such as in the movie Groundhog Day, the same day keeps getting repeated but with different outcomes each time because the character is changing/evolving.
I don’t know if a writer’s genre plays a role in whether they write linear or non-linear structure, but I know that I now write non-linear structure. I also don’t know if that’s necessarily good–for all I know it may be too confusing. But I find myself drawn to that type of story nonetheless.