Correct answer: They broke with the Catholic Church.
Additional context/details:
Luther and Calvin both proclaimed salvation as a gift of God's grace, rather than something earned by human efforts. The Roman Catholic Church spoke of God's grace also, but as an enabling power that helped human beings do the works required for obtaining salvation. The reformers (Luther and Calvin) still preached that we should do good works, but said those works were a fruit of being saved rather than a source of salvation.
Within the tradition of salvation by grace, there were key differences between Luther and Calvin, however.
Luther's emphasis was on what God's grace meant to the person who received that grace. He focused on justification by grace alone, and the fact that sinners were seen as innocent in God's eyes because of the life and death and resurrection of Jesus Christ. Luther had gone through his own personal struggle as a monk, feeling he was always under the judgment of God. But then he came to realize, from Romans 1:16-17, that "in the gospel the righteousness of God is revealed" that gives salvation apart from human works. This personal experience became the focus of his theology -- salvation as the free gift of God that lifts sinners from despair.
Calvin also taught that salvation was entirely by God's grace, but his emphasis was on what that meant to our understanding of God. As summarized by Evangelical Focus, "The real marvel of justification in Calvin’s thought was not that a sinner found himself (herself) pardoned from all iniquity but rather that God was being glorified through the salvation of such a transgressor. " So Calvin's emphasis in his teaching regarding salvation was as much about the glory of God as it was about the grace of God, while Luther focused on grace especially.
Another way of seeing how the difference between Luther and Calvin expressed itself would be to notice that Luther consistently emphasized the grace of God as the central point in all his teaching, where Calvin's central emphasis was on the sovereignty of God. This showed itself in their differing views on predestination. Both confessed, from the Bible, that God chose his believers from eternity, before time began. Luther emphasized only a positive side to this -- that it was a teaching all about God's grace. Calvin added a negative side to it also, that said God also chose from eternity the persons he would condemn to hell. He saw this as a testimony to God's sovereign power and freedom of choice.
