Between Orthodoxy and Catholicism, are there differences between them on how a person is saved?
Roman Catholicism tends to emphasize works. Protestantism tends to exclude works in favor of faith. Both tend to see salvation as a static state rather than as a process.
Orthodoxy takes a very different approach.
In the Scriptures the word "salvation" is used in two distinct yet inseparable meanings.
The first meaning of salvation is the Divine act of unmerited mercy by which we are freed from enslavement to death and sin. In this sense, we are saved by God-the-Son's incarnation, life, teaching, death, descent into Hell, resurrection, ascension, and sitting down at the right hand of the Father as a Person Who is by nature both God and man.
The instant a virgin called Mary conceived, the universe forever changed. God became one with His own creation. And because Satan has no power over God, Satan lost his grip on human nature.
In this sense, Orthodoxy proclaims and celebrates the victory of God over death and sin which frees all men from our ancient curse. All are saved. All are free from enslavement to death and sin. There is no corner of the earth nor any epoch of time which hides any man from God's saving labor. It is in this sense that we are "once saved, always saved."
Yet not all whom Christ saved will enter into the Kingdom.
Which brings us to the second way "salvation" is used in the Scriptures.
The second meaning refers to our free response to this gift God has given us.
To distinguish this second aspect of salvation, the early Church coined the term "theosis." Theosis is the process of personally achieving the potential of the human nature God created. If we define that nature by Genesis 1:26-27, then theosis is nothing less than our righteous God-ordained struggle to become God-like - to become living icons of our Creator. It is in this sense that we "work out our salvation with fear and trembling."
And, yes, that requires work!
Theosis involves fasting, prayer, self discipline, endurance, humility, courage, the pursuit of truth, and, above all, true love of God, of our fellow human beings, of all creation, and of ourselves.
Walking with Christ takes effort. It is a labor, a work. We follow Christ as soldiers follow their General, through heat and dust, through hunger and thirst, through fatigue, through battles against the evil one.
Baptism is the beginning of that labor. It is our rebirth and our regeneration. But Baptism is not the end of the process, nor is it a guarantee that we will complete the race.