Article: What’s the Difference Between Arminianism, Calvinism and Hyper-Calvinism? by Tom Ascol (original source the following summary reveals the basic differences between Arminianism, Calvinism, and hyper-Calvinism.

In one sense, hyper-Calvinism, like Arminianism, is a rationalistic perversion of true Calvinism. Whereas Arminianism undermines divine sovereignty, hyper-Calvinism undermines human responsibility. The irony is that both Arminianism and hyper-Calvinism start from the same, erroneous rationalistic presupposition, namely that human ability and responsibility are coextensive. That is, they must match up exactly or else it is irrational. If a man is to be held responsible for something, then he must have the ability to do it. On the other hand, if a man does not have the ability to perform it, he cannot be obligated to do it.

The Arminian looks at this premise and says, “Agreed! We know that the Bible holds all people responsible to repent and believe [which is true]. Therefore we must conclude that all men have the ability in themselves to repent and believe [which is false, according to the Bible].” Thus, Arminians teach that unconverted people have within themselves the spiritual ability to repent and believe, albeit such ability must be aided by grace.

The hyper-Calvinist takes the same premise (that man’s ability and responsibility are coextensive) and says, “Agreed! We know that the Bible teaches that in and of themselves all men are without spiritual ability to repent and believe [which is true]. Therefore we must conclude that unconverted people are not under obligation to repent and believe the gospel [which is false, according to the Bible].”

In contrast to both of these, the Calvinist looks at the premise and says, “Wrong! While it looks reasonable, it is not biblical. The Bible teaches both that fallen man is without spiritual ability and that he is obligated to repent and believe. Only by the powerful, regenerating work of the Holy Spirit is man given the ability to fulfill his duty to repent and believe.” And though this may seem unreasonable to rationalistic minds, there is no contradiction, and it is precisely the position the Bible teaches. The Calvinist view may appear irrational but in reality is supra-rational—it is revealed.