A Pure Evil is the worst of the worst. These people are abhorrent monsters who seek to cause chaos for their selfish and immoral gain and are completely irredeemable. They are the opposite of Pure Good. Here are their defining traits, as said on the Villains Wiki:
They have passed the Moral Event Horizon at least once (a term for when a character has shown they are irredeemable in the story).
They do not have true love for anyone and only care about themselves, if they claim to have love, that "love" is just perversion, possessiveness, or obsession.
Absolutely NOTHING justifies their actions, they are not positive at all, and they are beyond redemption.
These are just simple villains, Anti-Villains can never count, seeing how they play the role of a villain but have noble intent.
They know what they are doing are wrong, and they know what right and wrong is, but they only choose to do the latter.
They are not mindless beings of destruction (that would be a Generic Doomsday Villain), they have defined motives.
Person 1: So is Joker Pure Evil?
Person 2: Depends on which type, Person 1.