FUT Moments is a new FUT Mode that was added at the start of FIFA 23. The mode allows you to play different themed scenarios, complete thier challenges, and accumulate a unique FUT currency called Stars.
Imagine the FUT Moments mode as a book, and within this book are many distinct Stories, an example being Pitch Perfect. Within those Stories are multiple Chapters (or sometimes 1 chapter) that contain multiple Moments.
To finish each Moment scenario, Challenges (sometimes multiple) must completed. From completed Moments you will receive Stars, which you can redeem for rewards. Hopefully that makes it clearer, in this FUT Library explainer we'll get into the details.