In Roger Olson’s helpful review of Free Will Baptist theologian Matthew Pinson’s book, Arminian and Baptist: Explorations in a Theological Tradition, the distinction between “Reformed Arminianism” and “Wesleyan Arminianism” is described very helpfully. Olson explains that
Pinson’s book is a defense of “Reformed Arminianism” which he treats as the historical theological tradition of Free Will Baptists—as opposed to other Baptists and Wesleyans/Methodists. He appeals to Arminius himself to show that the Dutch theologian was firmly rooted in traditional Reformed thought even as he broke from the then (early 17th century) growing Calvinism of Beza and his followers over unconditional election, limited atonement and irresistible grace. And he appeals to Thomas Helwys and Thomas Grantham—early General Baptists—as precursors of contemporary Reformed/Free Will Baptist Arminianism. He drives a wedge between Helwys and John Smyth, for example, portraying the latter as a defector from the classical Protestantism of the Reformers.
Pinson posits that,
generally speaking, the Free Will Baptist tradition stuck with Augustinian-Reformed doctrines of original sin and satisfaction-substitutionary atonement and justification as imputation of Christ’s righteousness. According to him, Wesley, following certain Anglican Arminians, so amended these doctrines that his view and the majority of his followers, while still Arminian, left behind the Reformed tradition entirely.
So the upshot of Pinson’s argument is that there always has been a stream of Arminianism, going back to Arminius himself, that includes many Baptists, that is thoroughly Reformed with regard [to] original sin, human depravity, atonement and justification. This he calls “Reformed Arminianism” and he seeks to disassociate it from Wesleyan Arminianism.
I would add to the distinction the great importance of the Wesleyan doctrine of complete sanctification which I see as an innovation that does not derive from classic Arminianism.
Olson commends Pinson’s exposition of both Reformed Arminianism and the Free Will Baptist tradition, but he locates himself between Reformed and Wesleyan Arminianism, so he is much less critical of Wesleyan Arminianism than Pinson is. Olson also disagrees with Pinson in regard to open theism, and perhaps that disagreement illustrates a way in which Pinson is more Reformed in his Arminianism than Olson is. Olson thinks that Pinson is wrong to exclude open theism “from being considered truly Arminian,” and I agree with Olson, because I too have found that most evangelical open theists “wholeheartedly agree with basic Arminian soteriology.” I think that open theists are very consistent Arminians, and I agree with them that the classic Arminian doctrine of simple foreknowledge does not give God a significant advantage providentially when compared with open theism. On the other hand, Olson heartily agrees with Pinson “that ‘Molinism’ is inconsistent with the most basic impulses of Arminian theology. On this point, I am less certain of my own opinion than I used to be. Olson is very worried “about Arminians who use Molinism in a deterministic way or even open that door,” and I have been warming up to this suggestion by Olson, though I am naturally happy to see the direction of that movement, whereas it troubles Olson.