ExileTo exile an object, move it to the exile zone from wherever it is. See rule 406, “Exile.” (CR 701.13) the top X cards of your library. You may
castTo cast a spell is to take it from the zone it’s in (usually the hand), put it on the stack, and pay its costs, so that it will eventually resolve and have its effect. A player may cast a spell if they have priority. See rule 601, “Casting Spells.”
To cast a card is to cast it as a spell. (CR 701.5) instant and sorcery spells with mana value X or less from among them without paying their mana costs. Then put all cards exiled this way that weren't
castTo cast a spell is to take it from the zone it’s in (usually the hand), put it on the stack, and pay its costs, so that it will eventually resolve and have its effect. A player may cast a spell if they have priority. See rule 601, “Casting Spells.”
To cast a card is to cast it as a spell. (CR 701.5) into your graveyard.