Fire Emblem Fates - Special Edition was a limited time bundle containing both base stories, Birthright and Conquest, and gave access to DLC for the 3rd story, Revelation, when it became available.
The games were otherwise sold separately though you could get the second story path digitally at a discount.
You need to be have completed chapter 6 in the either game to access the other stories, and the DLCs, path.
Conquest is the hardest of the 3 paths having no ability to grind experience from maps, tougher mission objectives, and giving less money and experience for those missions. Birthright, the easiest path, has the ability to use scouting missions to grind experience and money and simpler mission objectives that give greater amounts of experience and money. Revelation is in the middle as the scouting missions are available but the mission objectives are similar to Conquest's. This is ignoring the 3 difficulty settings in-game.
"Two kingdoms at war – the peace-loving Hoshido and the glory-seeking Nohr – It’s up to the player to decide which side to take. As the prince/princess of Hoshido, who was raised by Nohr royal family, you will be torn between two families you love. Whichever path you take, you will face different types of challenges."