Purgatory: one version is, a place people go to suffer to pay for their sins, then they can go to heaven.
The Millennium: one version is, 1,000 years in which people really learn to repent of all their sins, then they can go to heaven. (This is basically the idea of the future implied by "MSLN".)
Taken generally, "purgatorial" is the notion that people need to suffer to overcome some sort of defect or deficit they have. "Millennial" is the notion that people need to learn in order to overcome those defects or deficits.
Sometimes it seems like it takes pain in order to learn certain lessons. It may be the case sometimes. But the Millenial point of view is that it's better to bring about learning without pain. Also, it may seem like you're accomplishing something by suffering. Maybe it makes you a better person. But if you're suffering without it making you a better person, it's probably unnecessary. Suffering can keep you from learning.
Sometimes you don't know how to not suffer. Or suffering is an unavoidable part of some pursuit that has to be pursued. Certainly there are things worth suffering for. But what is essential is inner change, not pain.