Augustine was a mover and shaker in the early Church and Pelagius was a monk who ended up being a labeled a heretic. Both had big differences when it came to Salvation. Pelagianism was repudiated by the Council of Carthage in 417.
To Augustine, God is the ideal of perfection. God is omnipotent. He exists outside of time, so the events of the past, present, and future are equally real to Him. All of Augustine's ideas about salvation can be drawn from these attributes. Because God is all good, then evil in the world must be the responsibility of human beings-the idea of Original Sin. Also, because God is both all-knowing and timeless, then He must have foreknowledge of who will be saved, and who will not. So, predestination is the logical conclusion. Since God is omnipotent, all-knowing and timeless, we cannot change God's mind to save us-we are saved by His will. This is the ground floor of Augustine's theory of Salvation.
Another big part of Augustine's salvation theology came from his idea of Original Sin. He puts all of his chips on this one concept: all evil exists because of Original Sin. Because of Original Sin, humans cannot do anything good on our own; free choice has been wasted by sin; our will can only do evil. Free will, in this case, is gone, because humans are only able to commit evil acts.
Augustine assumed that since humans cannot do good acts by their own choice, all good must be accomplished through the grace of God. The most vicious people may perform random acts of kindness, but only because God interjects. Likewise, the most saintly person quickly becomes immoral when God's grace leaves them, such as Peter's denying Jesus. So, it is through the workings of grace that we are saved, anything else would deny the sovereignty of God. Augustine basically said that if God had to save someone, then He wouldn't be God.
This is all well and good, but if we inherently cannot do good, how do we get the grace to be saved? According to Augustine there is only one answer: God gives it freely and with divine mercy. It does not make any difference about how much or how little faith one has, because God bestows faith.
Pelagius' idea of Salvation was grounded in freedom of human will, not God's sovereignty. Like Augustine, his ideas of salvation were closely related to Original Sin. Pelagius thought that Adam's sin was only an example of sin. It was not passed on to the rest of humanity. Rather than humans being forever corrupted by Adam's sin, Pelagius sees our fall from grace as humans becoming responsible for their own actions.
Augustine argued that, because of Original Sin, we can commit only evil acts that violate God's law. Pelagius, again taking a different stand, thought that humans were able to fulfill God's law. Since God knows our shortcomings and weaknesses as humans, He would not command things that we could not do. Grace, in Pelagius' view, was not a characteristic of the Saved, but was a type of assistance given by to those who chose to follow Him and live a life filled with good works. Augustine believed that God granted Faith and Grace freely, but Pelagius believed that God gives Grace to those who already have faith and are trying to live a godly life.
Pelagius did not believe that Salvation just happened, but happened through or as a result of the repentance of sins. Asking for forgiveness was not enough, it was not repentance. For Pelagius, it meant making a conscious effort to not sin again. Talk the talk, but walk the walk.
Obviously, you cannot perform good works just for the sake of some sort of hopeful calculation. The works must be real. And it is this belief-that we can use Jesus' example to become a better person and live a god-like life. That is where the big split occurs between Augustine and Pelagius.
The Eastern Orthodox Church's idea is that even though grace is required for men to save themselves, there is no such thing as total depravity, but there is still a moral ability within men that is not affected by original sin, and that men must work together with divine grace to be saved.