"Semi-Pelagian" is one of those terms that, like "hyper-Calvinism," gets thrown around a bit and abused. It has a (more or less) specific definition, however:
Doctrines, upheld during the period from 427 to 529, that rejected the extreme views both of Pelagius and of Augustine in regards to the priority of divine grace and human will in the initial work of salvation....
In opposition to Augustinianism, [John] Cassian taught that though a sickness is inherited through Adam's sin, human free will has not been entirely obliterated. Divine grace is indispensible for salvation, but it does not necessarily need to precede a free human choice, because, despite the weakness of human volition, the will takes the initiative toward God. In other words, divine grace and human free will must work together in salvation....
[Faustus of Riez] rejected the predestinarian conception of a divine monergism and taught that human will, by virtue of the freedom lett in it, takes the beginning step toward God. Salvation, therefore, is accomplished by the cooperation of human and divine factors, and predestination is merely God's foreknowledge of what a person has freely decided. Grace, to Faustus, meant the divine illumination of human will, and not, as it did to Augustine, the regenerative power of grace in the heart. (Richard Kyle, "Semi-Pelagianism," Evangelical Dictionary of Theology, ed. Walter A. Elwell [Grand Rapids: Baker, 1984], 1000-01.
Another source:
John Cassian (ca. 360–ca. 435), a monk, endeavored to find a compromise position by which the human will and the divine will could cooperate in salvation. He taught that all men are sinful because of the Fall and that their wills are weakened but not totally corrupted. Man’s partially free will can cooperate with divine grace in the process of salvation. He feared that the doctrines of election and irresistible grace taught by Augustine might lead to ethical irresponsibility. The view of Cassian was condemned at the Synod of Orange in 529 in favor of a moderate Augustinian view. (Earle E. Cairns, Christianity Through the Centuries, 3rd ed. [Grand Rapids: Zondervan, 1996], 132.
So to compare and contrast the three views:
Topic | Pelagian | Semi-Pelagian | Augustinian |
Original sin | Rejects the idea of original sin. Every human being is born into an innocent and unfallen state. | All humanity has been affected by the fall, but the ability to choose the good is not completely destroyed. | The fall destroyed the moral image of God in humanity, and all humans are dead to God and helpless to change their state. |
Free will | With no corruption due to sin, the will is completely free to choose to obey God's commandments or not. | The freedom of the will is damaged, but not destroyed. People have the ability to repent and believe if they choose. | The human will is enslaved to sin and inclined only to choose sinfully. |
Grace | Unnecessary for salvation. Every person is innately capable of fulfilling divine commands and becoming a follower of Jesus. | Necessary for salvation, but not for the initial step toward God. | Necessary for salvation, because human beings dead in sin have no capacity to move toward God on their own. |
Predestination | God knows who will freely choose to be saved. | God knows who will freely choose to be saved. | God knows whom he will choose to save. |
Synergistic/monergistic | Synergistic | Synergistic | Monergistic (God's work alone) |
There's also a fourth position,
semi-Augustinianism, which is essentially the same as semi-Pelagianism, except that God rather than man takes the initiative, and the human and divine wills then cooperate to bring about salvation.