The Remonstrant controversy was a battle of giants. In its earnest grapple, the movement tentatively begun by Arminius tended rapidly toward its level in a distinctively Pelagian anthropology and Socinian soteriology. But in the great evangelical revival of the last century [18th century; Warfield wrote this at the end of the 19th century], the Wesleyan leaders offered to the world an Evangelicalized Arminianism. The rationalism of the Remonstrants, they affirmed, was not due to their Arminianism but to their Humanism. The essential elements of Arminianism, they asserted, were in no wise inconsistent with the great Evangelical doctrines of sin and atonement. On the contrary, they declared, the Arminian construction alone gave their full rights to the catholic doctrines of the condemnation of all men in Adam and the vicarious satisfaction for sin in Christ. An Arminianism zealous for these doctrines might well claim to stand on a higher plane than that occupied by the Remonstrants. The question, however, was a pressing one, whether the Evangelical elements ought to rule to the exclusion of the unharmonizable Arminian principle, in which case we should have consistent Calvinism; or else the Arminian principle would inevitably rule to the exclusion of the Evangelical doctrines forced into artificial conjunction with it, and we should have consistent Arminianism. After a century of conflict, Dr. Miley's [a Wesleyan Arminian theologian] admirably reasoned volumes come to tell us frankly that the Calvinists have been right in these contentions. Arminianism, he says, has no logical place in its system for a doctrine of race sin either in the sense of the participation of the race in the guilt of Adam's first sin, or in the sense of the infection of the race with a guilty corruption. Arminianism, he says, has no logical place in its system for a doctrine of penal substitution of Christ for sinners and of an atonement by satisfaction. If the Arminian principle is to rule, he says, the doctrine of race sin must go, and the doctrine of vicarious punishment must do. And, as he thinks that the Arminian principle ought to rule, he teaches that men are not by nature under the condemning wrath of God, and that Christ did not vicariously bear the penalty of sin. Thus, in his hands, Arminianism is seeking to purify itself by cleansing itself from the Evangelical elements with which it has been so long conjoined. [B.B. Warfield, "A Review of John Miley's Systematic Theology," in Selected Shorter Writings, 2:314-5; Bold added]
Contrary to modern "Evangelical Arminians," it has long been known that there is a qualitative difference between the Classical Arminians or the Remonstrants, and the Wesleyan or Evangelical Arminians.