Smash 4 had perfect pivots, but those aren't in Ultimate. If I remember correctly, the only mechanics returning from Smash 4 are rage, ledge trumping, and 2-framing.
Rage is a passive ability all characters have that gradually boosts the knockback of their moves as their percent rises. Rage starts scaling at 35% and maxes out at 150%, at which point the knockback on your moves will have a multiplier of 1.1x. In Smash 4, the multiplier at 150% was actually 1.15x, but that turned out to be too much, so it was nerfed accordingly. Rage doesn't affect damage and it does stack with Lucario's aura in case you were wondering.
Ledge trumping is basically the replacement for ledge hogging. Now when a player is hanging from a ledge and someone else tries to grab it, the former will be forced off in favor of the latter. In Smash 4, this would often lead into a guaranteed back air against the player who was forced off if they didn't immediately buffer a getup option, but since you can actually DI during the ledge trump animation now to avoid an oncoming attack, it's more of a rare mixup than a true follow up. This change allows tether recoveries to not get completely shafted, so I think it's very welcome.
Finally, 2-framing refers to hitting an opponent during the two frames of vulnerability that they receive right before grabbing the ledge. It's pretty difficult to time unless you have a long-lasting hitbox like Lucas's down smash. Every character in the game has these two frames of vulnerability... well... usually. There are two main exceptions. Firstly, if you use a tether recovery, you'll be vulnerable right up until your character touches the ledge, but you won't receive any additional frames of vulnerability after that. Secondly, if you have a teleport recovery and recover from
above the ledge, you'll get ledge invincibility right away. There are some more small exceptions, but they'll rarely come into play. Watch this video if you want to learn more about it:
https://www.youtube.com/watch?v=-uQn19zvWpo
