Draft
Card drafting is the proces where players pick cards from a limited subset, such as a common pool, to gain some immediate advantage or to assemble hands of cards that are used to meet objectives within the game. Games where cards are simply drawn from a pile are not card drafting games - drafting implies that players have some sort of choice.
The most commonly known draft format in Magic: The Gathering is Booster draft. But there are many Casual variants, as well.