What are the differences between Fire Emblem Fates: Birthright, Fire Emblem Fates: Conquest, and Fire Emblem Fates: Revelation

As bwDraco said, they are all different stories but there is more to it than that. Each campaign has a unique set of playable characters that can only be used in that campaign (most notable are the Hoshido/Nohr families from the game covers. They can only be used in their respective campaigns). There are a few serious gameplay differences between Birthright and Conquest as well. Birthright plays much more like Awakening, putting serious focus on the more "JRPG" aspects of the game - world map, level-grinding, more focus on shipping characters, and generally is played much more like an RPG than a strategy game.

Conquest, on the other hand, keeps to the series' roots much more strictly. From what I understand, Conquest is a linear progression through the story, meaning once you complete a chapter, you can't go back using the world map. Conquest is also more difficult as it is meant to be played much more like a strategy game than an RPG with strategy elements. If you're familiar with some of the older games, Conquest will be pretty similar to those. However, if you've only played Awakening, Conquest may be a bit of a shock at first at how different it is compared to Awakening.