Dragons can be categorized by rarity. The rarity of the dragon not only dictates how common the dragon will be and where it can be obtained but will also determine the level of power said dragon has. For instance, dragons of higher rarity can be more effective at collecting resources and attacking in Defend Berk. They will also yield more resources or scales when released or ascended. You can learn more about different rarities here.
 
Dragons may also be categorized by their type. The type indicates where the dragon came from and if it belongs to a larger group. Most dragons obtained through normal means have no type. However, all dragons received through collections or Brawl have a type. You can read more about types here.