Protestant Christians can usually be divided into two camps. There are those who follow John Calvin and those who follow James (Jacobus) Arminius. Calvin lived during the time of the reformation (1509-1564), while Arminius lived a generation later, (1560-1609). They were both theologians, both had a deep faith in Jesus, but they were diametrically opposed in their theology.
Calvin's followers were called Calvinists. Churches that adopted Calvinist teachings were called "reformed". The Anglican church is such a church. Cranmer, the founding Bishop of the Anglican church, was a convinced Calvinist and so the Thirty Nine Articles, found at the back of our Prayer Book, reflect Calvinist teaching. The Synod of Dort in 1619 established the "Five Points" of Calvinism. They are: i] The total inability of anyone to believe the gospel without a preliminary work of the Holy Spirit and the gift of faith. ii] Unconditional election ("effectual call") - God's choice of particular people for salvation. iii] Limited atonement - Jesus died for the elect only. iv] Irresistible grace - God's irresistible inward call to salvation. v] Perseverance of the saints - all who are chosen by God are eternally saved. They persevere to the end.
Arminius' followers were called Arminians. After his death his followers agreed to the "remonstrance" in 1610, which was the subject of debate at the Synod of Dort in Holland in 1619. Arminian teaching was to dominate the Methodist revival in England and so became the dominant theology of the American churches after the work of the early Methodist missionaries. Evangelicals (Methodists who stayed in the Anglican church during the "great awakening" in the late 1700's in England) tended to be Calvinist. The Five Points of Arminianism are: i] Although human nature was affected by the fall, people are capable of freely responding to the gospel in faith (their personal trust in the Jesus). ii] Conditional election - God's choice of particular people for salvation is based on his foreknowledge that they will believe the gospel. iii] General atonement - Jesus died for everyone, making it possible for everyone to be saved. iv] Resistible grace - the Spirit's inward call can be resisted. v] Falling from grace - a believer can lose their salvation (Arminius himself was not so sure about this).
It is most likely that both sides of the debate have got some of the truth, and both sides have got some of it wrong. In the end, God is sovereign and humans are free.