While both of these men had very different styles of international relations as well as different ideologies for approaching them, they were both master negotiators that achieved some lasting agreements between and with foreign governments.
Both Carter and Reagan successfully negotiated nuclear arms treaties with the Soviet Union, although Carter was more successful in peace negotiations, such as the Camp David Accords between Israel and Egypt. Carter took the logical approach to differences with foreign leaders, while Reagan liked to negotiate from a position of economic and military strength.
I think that the first answer does a good job of going over the two men's differences, but it does overlook one important similarity. This is that both men were political "outsiders," at least in terms of the federal government.
In the years right after the Vietnam War and Watergate, there was a great deal of distrust of the federal government and of "insiders." Both Carter and Reagan were able to exploit that distrust. Although they had both been governors, neither had had any major position in the federal government. Because of this, they were both able to run as reformers who would change the way things worked in Washington.
Outside of the fact that both men served as Presidents of the United States, I find it a bit challenging to find much in way of common ground between them. Carter was the last vestige of the Democratic Liberalism that defined the party's politics for so long prior to his Presidency. Reagan's political philosophy was defined in stark contrast to the ideas that Carter was advocating with his work as President. Reagan believed in a minimalist approach of government, while Carter envisioned a more active role for government. From a foreign policy point of view, Carter had a difficult time advocating America's presence in the world, while Reagan sought to increase American presence in a defiant and manner that represented strength and dominance. Carter never was able to fully embrace the "exceptionalism" that was such a strong part of Reagan's administration and philosophical approach. I would also say that one of the strongest points of difference between both leaders is that Carter struggled with trying to balance the different demands of different groups in America. Carter tried to increase governmental effectiveness in dealing with urban centers, as well as the suburban element. Reagan seemed to have no problem advocating a policy- based point of view that was open about its willingness to not support urban centers and renewal and embrace the suburban element from an economic and social point of view. Consider that Carter's "malaise" idea would have never been advocated by Reagan and his vision of American exceptionalism.