Stories are categorized into two main groups; Main Stories and Event Stories. Aswell as some others such as Side Stories and Special Stories.
Main Stories
The first 5 chapters of all Main Stories are always available, and the rest will become available as you increase a unit's rank.
Event Stories
The first chapter of an Event story will be available right as the event debuts, and the rest will be available as you earn event points.
Side Stories
Side Stories are unlocked with Attribute pieces and Attribute gems through individual cards that you own. They provide rewards and increase the card's overall power.
Special Stories
Special Stories are oftentimes limited log-in stories during specific events (e.g. Collaborations, Anniversary countdown).