Story Mode lets you experience a sequence of progressively harder missions that follow a storyline. In Feud it’s often used to introduce (and unlock) new characters which you can use in the other play modes. Story mode missions also have a hard difficulty that introduces new groups of enemies changing the dynamic of fights.
The Hatfield Story is where you begin. It takes you through the basics of Feud and opens up into harder challenges as you move into the later missions.
In the McCoys story you’ll meet the other half of the Feud and a couple new enemy types that make things more challenging.
The Uneasy Alliance brings both families together in a rare truce that sees them leaving the mountains and forests behind and heading out West to face a new threat.