Arminianism is most commonly thought of as the belief that although God knows the future, God also allows free will in future actions. In this belief, adherents are able to maintain both the Classical attributes of God (such as Omniscience) while also maintaining the Classical attributes of man (Free Will). See the Church Fathers on Free Will.
Open Theism is the belief that God is free to choose not the know the future. In order to introduce Open Theism to people, I often ask: “Can God do anything?” and then follow it up with “Can God choose not to know something?”. When it is put in the manner, people are forced to weigh their conflicting beliefs about God. Is God free to learn new thoughts, create new things, locate Himself where He wants? If not, is God all powerful? Open Theism is about if God is free.
Critics and some Open Theists describe Open Theism as the belief that the future is not set. To me, that is a strange way of defining the issue. After all, isn’t the primary purpose of the Bible to tell us about God? Isn’t the core issue about who God is? I am not an Open Theist due to philosophical reasons or because I am particularly attached to philosophical notions about the future. I am an Open Theist because I believe the Bible is the source of our knowledge about God and the Bible does not present God in the Classical image.
The difference then, between Arminianism and Open Theism primarily comes down to how attached each are to the Classical attributes of God. Arminianism wants to maintain the attribute of Omniscience while trying to maintain the truth of select Old Testament stories about God (in relation to His emotions and appeals to man for repentance). They spiritualize texts that describe God’s surprise about the future, God’s reliance on others (such as when God asked angels for advice in 1 Kings 22), and God’s repentance. They hold as literal God’s emotional outbursts, God’s unending appeal to His people to repent, and God’s blamelessness for evil.
Open Theism, on the other hand, discards the traditional understanding of Omniscience (some Open Theists try to redefine Omniscience in order to maintain use of the word). The philosophical contingent of Open Theists maintain God is more righteous and better understood as Open. The fundamentalist contingent of Open Theism holds that all Old Testament stories about God are true, regardless of the implications. Myself, and select other Open Theists, take it a step farther and claim that if God wants to not know current events, that is His prerogative. For example, if God does not want up-to-the-minute updates on the wickedness of Sodom, He does not have to have it. If God then wants to go see if Sodom is as evil as He hears, He can go do that. There is no alternative figurative meaning to Genesis 18, in which this exact event is described.
Although there is a large contingent of Open Theists that do not take the Bible literally (they do not maintain that the face value communication of the writers to the reader always reflects reality), the more that someone accepts the Bible as literal, the more they have to affirm Open Theism. The case of Sodom being exhibit one.
The difference between Open Theism and Arminianism fundamentalism is how willing one is to spiritualize the text in order to maintain a Classical understanding of Omniscience. The difference between Open Theism and Arminianism spiritualists is how one values God’s interactions with humanity.