Q: Some cards say things about “when discarded”. If I use Zap A Card, the card isn’t discarded, it’s just no longer in play. Isn’t that the same thing in this case?

A: Yes, removing a card from play with Zap A Card would trigger the same effect as discarding it.

Cards that have an actionable effect when discarded:
Double Agenda: Whoever takes this out of play decides which Goal remains in play.
Triple Agenda: Whoever takes this out of play decides which Goal remains in play.
Arkham Asylum: Whoever takes this out of play shuffles whatever Villains are under it, and deals them out to everyone, starting with whatever player they want.
Central Axis: Whoever takes this out of play takes whatever Keeper is currently the Central Axis, and puts it in play in front of them.
Camouflage: When this is taken out of play, everyone turns their face-down Keepers face-up again.