Yes, there are other systems. These two, historically speaking, have been two of the bigger views --at least in the past 500 years.
Feel free to disagree with either or both.
|Free-Will or Human Ability|
Although human nature was seriously affected by the fall, man has not been left in a state of total spiritual helplessness. God graciously enables every sinner to repent and believe, but He does not interfere with man's freedom. The sinner has the power to either cooperate with God's Spirit and be regenerated or resist God's grace and perish. The lost sinner needs the Spirit's assistance, but he does not have to be regenerated by the Spirit before he can believe, for faith is man's act and precedes the new birth.
|Total Inability or Total Depravity|
Because of the fall, man is unable of himself to savingly believe the gospel. The sinner is dead, blind, and deaf to the things of God; his heart is deceitful and desperately corrupt. It takes regeneration by which the Spirit makes the sinner alive and gives him a new nature. Faith is not something man contributes to salvation but is itself a part of God's gift of salvation.
God's choice of certain individuals unto salvation before the foundation of the world was based upon His foreseeing that they would respond to His call. He selected only those whom He knew would of themselves freely believe the gospel. Election therefore was determined by or conditioned upon what man would do. The faith which God foresaw and upon which He based His choice was not given to the sinner by God (it was not created by the regenerating power of the Holy Spirit) but resulted solely from man's will. It was left entirely up to man as to who would believe and therefore as to who would be elected unto salvation. God chose those whom He knew would, of their own free will, choose Christ. Thus the sinner's choice of Christ, not God's choice of the sinner, is the ultimate cause of salvation.
God's choice of certain individuals unto salvation before the foundation of the world rested solely in His own sovereign will. His choice of particular sinners was not based on any foreseen response of obedience on their part, such as faith, repentance, etc. On the contrary, God gives faith and repentance to each individual whom He selected. These acts are the result, not the cause of God's choice. Election therefore was not determined by or conditioned upon any virtuous quality or act foreseen in man. Those whom God sovereignly elected He brings through the power of the Spirit to a willing acceptance of Christ. Thus God's choice of the sinner, not the sinner's choice of Christ, is the ultimate cause of salvation.
|Universal Redemption or General Atonement|
Christ's redeeming work made it possible for everyone to be saved but did not actually secure the salvation of anyone. Although Christ died for all men and for every man, only those who believe on Him are saved. Christ's redemption becomes effective only if man chooses to accept it.
|Particular Redemption or Limited Atonement|
Christ's redeeming work was intended to save the elect only and actually secured salvation for them. His death was substitutionary endurance of the penalty of sin in the place of certain specified sinners.
|The Holy Spirit Can Be Effectually Resisted|
The Spirit calls inwardly all those who are called outwardly by the gospel invitation; He does all that He can to bring every sinner to salvation. But inasmuch as man is free, he can successfully resist the Spirit's call. The Spirit cannot regenerate the sinner until he believes; faith (which is man's contribution) proceeds and makes possible the new birth. Until the sinner responds, the Spirit cannot give life. God's grace, therefore, is not invincible; it can be, and often is, resisted and thwarted by man.
|The Efficacious Call of the Spirit or Irresistible Grace|
In addition to the outward general call to salvation which is made to everyone who hears the gospel, the Holy Spirit extends to the elect a special inward call that inevitably brings them to salvation. The internal call cannot be rejected; it always results in conversion. The Spirit graciously causes the elect sinner to cooperate, to believe, to repent, to come freely and willingly to Christ. God's grace, therefore, is invincible; it never fails to result in the salvation of those to whom it is extended.
|Falling from Grace|
Those who believe and are truly saved can lose their salvation by failing to keep up their faith, etc. All Arminians have not been agreed on this point; some have held that believers are eternally secure in Christ - that once a sinner is regenerated, he can never be lost.
|Perseverance of the Saints|
All who are chosen by God, redeemed by Christ, and given faith by the Spirit are eternally saved. They are kept in faith by the power of Almighty God and thus persevere to the end