Answer
Actually, both goats represent both expiation and propitiation. Expiation is how the atonement affects man; propitiation is how the atonement affects God -- man's sin is forgiven, covered, removed (expiated); God's wrath and justice are satisfied (propitiated). Both goats contain elements of each, though perhaps each one bears a different emphasis: the Lord's goat is slain, perhaps emphasizing the satisfaction of God's wrath (but also the elimination of Israel's sin in that the goat is a "sin offering"); the scapegoat is exiled bearing sin on its back, perhaps emphasizing the removal of man's sin and guilt (but also emphasizing God's judgment in casting the goat from his presence).
The two goats may also be seen as parallels to two different types of judgment on sin: death and exile. The worst corporate covenant curse (the worst one affecting Israel as a whole people) was exile from the Promised Land, which parallels the scapegoat's exile into the wilderness because of the it bore. The worst individual covenant curse was death (both temporal and eternal), which parallels the death of the Lord's goat.
Answer by Ra McLaughlin
Ra McLaughlin is Vice President of Finance and Administration at Third Millennium Ministries.