Wesleyanism and Classical Arminianism have much in common, however, there are a few differences. Here's a list that compares some of the differences in belief. These are generalities, as particular beliefs often vary from person to person. And some of these categories overlap a bit. For example: One's view of sanctification influences one's view of righteousness.
Sanctification / Holiness: Wesleyans place an emphasis on entire sanctification (although perhaps less so though than they used to). Classical Arminians do not hold to entire sanctification. Wesleyans teach that Christians can be completely sanctified in this lifetime, and can live a holy life. Sanctification is not only inward, it is also outward, and motivates a life of service. John Wesley called this "Holiness of Heart and Life". Some Wesleyans see this as a process. Some see it as an instant second work of grace. Some a combination of the two. J Kenneth Grider has a book about this. Entire Sanctification: The Distinctive Doctrine of Wesleyanism.
Atonement: Wesleyans often hold to the moral government view of the atonement. Jesus suffered and died as a governmental act to show that God was displeased with the sin of man. Anyone who accepts the suffering of Jesus will be saved. Classical Arminians usually hold to substitutionary atonement. Jesus died as a substitute for mankind, taking our place. Those who believe will be saved. It should be noted that John Wesley himself held to substitutionary atonement. However, most of his followers have held to the governmental view, particularly since the late 1800's. This was the view originally articulated by the Remonstrant Hugo Grotius, and later advocated by evangelist Charles Finney, and Methodist theologian John Miley.
Forfeiting Salvation: Wesleyans believe salvation can be forfeited by a deliberately sinful life. It can be regained by repentance. Classical Arminians have different opinions on the matter. Some agree with Wesleyans that salvation can be forfeited and regained. Some believe that if salvation is forfeited it cannot be regained again. Some believe that salvation cannot be forfeited. Arminius himself never took a position on this issue. As a side note, I think there is a trend toward identifying with Classical Arminianism among some in the SBC, because they can still hold to "once saved always saved". This is good. Calvinism has become very divisive among the SBC and the folks who believe that Jesus died for the world are taking another look at Arminianism.
Righteousness: Wesleyans believe in imputed righteousness and imparted righteousness. Classical Arminians generally hold to only imputed righteousness. Imputed righteousness is a forensic righteousness before God. It teaches that that we are still sinful at heart after becoming Christians, but God the Father ignores our sin because of our faith in Jesus. When he looks at us he sees the righteousness of Jesus instead of our sin. Imparted righteousness teaches that we are acceptable to the Father because the blood of Jesus has really made us pure and has changed us inside. We are holy in God's sight because Jesus has genuinely made us so.
Spirit Focus: Wesleyans place a priority on the indwelling of the Holy Spirit and gifts of the Spirit (healing, prophesy, etc). Charismatic Wesleyans also hold that the gift of tongues is one of the evidences of the filling of the Spirit. Classical Arminians believe in the filling of the Spirit, but generally have less focus on gifts of the Spirit.
Foreknowledge: Wesleyans are more friendly to open theism, although many also hold to classical foreknowledge. Open theism teaches that God does not exhaustively know the future because the future is open and cannot be known. Classical Arminians believe that God exhaustively knows the future.
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