It's not when its cast it's when it enters the battlefield. But yes both triggers go off.
January 13, 2022 8:55 a.m.
There's two separate effects at play:
Whenever Fell Specter enters the battlefield, target opponent discards a card.
Whenever an opponent discards a card, that player loses 2 life and you gain 2 life.
Ability 1 happens once when the creature is cast, not countered, and enters the battlefield, and will always happen, even if you would Murder the Fell Specter in response to its trigger, target opponent still discards a card.
Ability 2 is a static effect, meaning as long as the Fell Specter is on the battlefield, every card discarded will create a trigger for the life loss.
When Fell Specter enters the battlefield, it makes 1 happen. Because it's on the battlefield after entering, 2 will happen too, as a direct result as one. However, when target opponent is already empty-handed, and doesn't actually discard a card, 2 will not trigger.
When the Fell Specter is destroyed after entering the battlefield, but before the discard trigger has resolved, ability 2 will no longer trigger from the discarding, because the creature is no longer on the battlefield the moment the discarding happens.
So if you play Fell Specter, and it enters the battlefield, the discard trigger goes on the stack, and you point out who you target with it. Then there's an opportunity for other players to respond. If nobody does respond, the target will discard if able, and lose life accordingly. However, if an opponent uses Murder on the Fell Specter before discarding happens, the creature will die and not be on the battlefield anymore when the discard happens. Then target opponent still discards a card to the trigger, but no life will be lost and gained because of it anymore.
So generally, you are right that both will happen with nobody interfering. But because both are caused by different lines of text, you can prevent one of the two from happening, with instant speed removal.
January 13, 2022 9:50 a.m.
Thanks a lot, fellow wizards! Especially for the thorough analisys!
January 13, 2022 12:36 p.m.
In the future, the "Rules Q&A" section at the top of the page (or in the drop-down list from the three lines on mobile) is the place for this sort of thing. Thanks!
January 14, 2022 1:54 a.m.
Just one clarification of the big answer up there: Fell Specter does not gain you life. Even if you give it lifelink, it will only gain you life when it deals combat damage, because the trigger is making the opponent lose life, not dealing damage to them.
January 15, 2022 9:58 a.m.
Polaris: lifelink is not limited to combat damage, it can apply to any damage. granted this situation is life loss and not damage, but i thought it worth mentioning that lifelink can apply to non-combat damage.
January 16, 2022 2:58 p.m.
In the future, please remember to hit the green "Mark as Answer" button to indicate your question is resolved. Since this question has been resolved for a number of days, I have gone ahead and marked an answer on your behalf.