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 spell. If a permanent spell is countered this way,
exileTo exile an object, move it to the exile zone from wherever it is. See rule 406, “Exile.” (CR 701.13) it instead of putting it into its owner's graveyard. 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) that card without paying its mana cost for as long as it remains exiled.