Monster abilities
A creature's special attacks run through the same machinery as a player's spells, so each one has its own page under Spells with its numbers on it - dragon breath, beholder rays and the antimagic cone, troglodyte stench, the tyrant fog, and the rest.
Auras
An aura is not cast at you: it sits on the creature and catches whoever is inside it, round after round. The creature is never caught by its own.
The saving throw is 10 + half the creature's hit dice + an eighth of them again. A level 40 creature therefore asks for a 35, and nothing about your own level makes that easier. (A player carrying the same aura adds half their Wisdom modifier on top.)
What the aura does when you fail depends on which it is - fear, blinding, stun, menace, the unearthly visage, the unnatural aura, horrific appearance, doom, acid - and several of them cap their duration however powerful the creature is: the fear aura, for instance, never holds anyone for more than three rounds.
Boss mechanics are separate
The things a boss does on a timer - pillars, exploding adds, waves - are not auras and not spells. They are on Bosses.