In 2024 and in A5E, it's an attack roll make an unarmed attack (which can inflict higher damage with certain feats or class features) but a saving throw for your opponent for the others. No more expertise in Athletics or advantage from being berserk. It makes it more of a fair contest. The main difference in A5E (there are a few others like being able to shove more than 5 feet)is that you ALSO do the basic 1 damage when you do the other manoeuvres if they fail their save."A melee attack that involves using your body to damage, grapple, or shove a target within 5ft of you."
Hmmm...
Though the Damage option -does- specify that you have to make an attack roll, separately from the introductory text.
I'll accept this interpretation because it's marginally less lame for D&D24 than the alternative... but A5e's implementation remains superior, IMO.
Though I almost can't wait to see some funky interactions since grappling is a melee attack tied to unarmed strike when someone implements a mechanic that applies to all melee attacks and results in someone pulling off a flaming Piledriver of a grapple check 'cause it "Adds 3d6 fire damage to all melee attacks!"
So no features that require an attack roll or a damage roll will key off of these manoeuvres unless expressly stated.