[Semi-Pelagianism]
While not denying the necessity of Grace for salvation, Semi-Pelagianism maintains that the first steps towards the Christian life are ordinarily taken by the human will and that Grace supervened only later.
[Arminianism]
In contrast to semi-pelagianism,
Arminianism teaches that the first steps of grace are taken by God. This teaching derives from the Remonstrance of 1610, a codification of the teachings of Jacob Arminius (1559-1609). Here are the 3rd and 4th articles of five
to show how close it actually approaches traditional Calvinism, but still leaves man with a small island of righteousness, as it affirms that unregenerate man can think spiritual thoughts, perceive the beauty and excellency of Christ, create affections for Him and thus turn in faith to Him, apart from the quickening of the Holy Spirit. They affirm that God's grace is always resistable, therefore, when one believe, it is not grace which makes one to differ from another, but naturally produced faith:
III.
That man has not saving grace of himself, nor of the working of his own free-will, inasmuch as in his state of apostasy and sin he can for himself and by himself think nothing that is good--nothing, that is, truly good, such as saving faith is, above all else. But that it is necessary that by God, in Christ and through his Holy Spirit he be born again and renewed in understanding, affections and will and in all his faculties, that he may be able to understand, think, will, and perform what is truly good, according to the Word of God [John 15:5].
IV.
That this grace of God is the beginning, the progress and the end of all good; so that even the regenerate man can neither think, will nor effect any good, nor withstand any temptation to evil, without grace precedent (or prevenient), awakening, following and co-operating. So that all good deeds and all movements towards good that can be conceived in through must be ascribed to the grace of God in Christ. But with respect to the mode of operation, grace is not irresistible; for it is written of many that they resisted the Holy Spirit [Acts 7 and elsewhere passim].
http://www.monergism.com/thethreshold/articles/onsite/Arm_Semi_Differences.html