As an additional cost to
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) this spell,
sacrificeTo sacrifice a permanent, its controller moves it from the battlefield directly to its owner’s graveyard. A player can’t sacrifice something that isn’t a permanent, or something that’s a permanent they don’t control. Sacrificing a permanent doesn’t destroy it, so regeneration or other effects that replace destruction can’t affect this action. (CR 701.21) a legendary creature or pay
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CounterTo counter a spell or ability is to cancel it: remove it from the stack without resolving it. A counter on an object or player is instead a marker that changes characteristics or interacts with rules or abilities; for example, a +1/+1 counter modifies a creature’s power and toughness. (CR 701.6; 122.1) target activated ability, triggered ability, or noncreature spell.