Sea of Thieves does not follow a typical storyline. The game doesn't have an overarching linear plot. However, it does feature smaller stories that can be completed during a playthrough. They are narrative and follow similar quest styles from other adventure games.
In addition to standard quests, procedurally generated quests are also present. Looking for sunken ships, buried treasures, and other objects may take you off course and into unfamiliar territory!
Voyages are considered to be Quests in longform. These will take significantly longer than a quest.