A drafting game that isn’t a deckbuilder or set collection? That exists, and its name is Enchanters: Overlords.
Adventure Board Games
Adventure games are a heavily-themed genre in which players, each controlling a single character, compete with both each other and non-player foes. They often follow a tiered progression, in which easier objectives must be completed in order to gain access to harder objectives, leading up to a single culminating event which grants victory to the player who achieves it. Adventure games are frequently themed around fantastical or improbable events, with a strong narrative component. Players may have asymmetrical character abilities, though this is not a requirement for the genre. Older adventure games, such as Talisman, made heavy use of roll-and-move mechanics, random events, and dice rolls in order to ensure that players had a more or less equal chance at victory.
Let's take a look at Vigilante. It’s a game about superheroes, social deduction, and card combos.