The story owner can edit all chapters of a story, no matter who the author is. (The story owner is usually the author who posted the first chapter of a story.)
The story owner can also assign the story role Editor to users of their choice. Editors can edit all chapters of a story as well. (Currently, there is no way to see who are the editors of a story.)
If you add a chapter to a story, the author of the previous chapter isn't necessarily the story owner or an assigned editor. If they don't have either of these roles, they can't edit your chapter.
If a story uses the mode Moderated, your chapter will be In Review after you published it. Then, it must be approved by the story owner or an editor of the story before it becomes publicly visible.
Before they approve it, they might or might not edit the chapter. They could also reject it and tell you what they would like you to change.
If your chapter is unpublished (i.e. in draft mode, not in review), the story owner and Editors can access them. But they can't see draft chapters on the story map, so they might need a direct link or the link of the parent chapter.