The primary differences between Lutheranism and Calvinism are that the Calvinists believed in predestination while the Lutherans did not, that the Calvinists believed in the supreme authority of religion while the Lutherans did not, and that the Lutherans believed in transubstantiation while the Calvinists did not. These two religions and doctrines evolved from other Christian religions during the Protestant Reformation.
Predestination is the idea that regardless of what a person does, he or she is destined for either salvation or damnation. Calvinists and other religions who believe in predestination believe that God has already chosen their path and already willed for them to either live a good Christian life that leads to heaven or a poor Christian life that leads to hell. Calvin said that a person could tell if he or she were among one of God's chosen ones if, despite all of the bad things in the person's life, he or she kept following the saintly path.
The idea of supreme authority of religion was also Calvin's idea. Calvin believed that the secular government should not have any say over the church and he wanted a theocracy government. Luther, on the other hand, believed that the church should follow the secular laws to help keep the public order and to allow people the freedom to worship in their own way.
The transubstantiation rule is something that many Christian religions review. Luther, when breaking away from the Catholic Church, decided to keep transubstantiation. Calvin did not believe in the idea that God was physically present in communion and believed that God was only spiritually present, which is known as consubstantiation.