Whenever you
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) an artifact, instant, or sorcery spell, copy that spell. You may choose new targets for the copy. This ability triggers only once each turn. (A copy of a permanent spell becomes a token.)
Whenever an opponent casts an artifact, instant, or sorcery spell,
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) that spell. This ability triggers only once each turn.