How did President Carter's foreign policy approach differ from that of Nixon and Ford?
Nixon's foreign policy was largely the product of what is typically called the "realist" approach, with its formulation the product of the of Nixon's view of world affairs and the academic theories applied by Henry Kissinger. Against the backdrop of the war in Vietnam and the Cold War, Nixon and Kissinger sought less to advance U.S. interests than to protect them from the perceived threat of Soviet expansionism. With a U.S.-dominated alliance unifying Western Europe and a Soviet-dominated "bloc" comprising the captive nations of Central and Eastern Europe, the European continent was stablized along the inter-German line separating East from West. The threat of nuclear war served as a check on large-scale military confrontation along that frontier.
While Europe enjoyed such "balance of power" stability, the developing world enjoyed no such stability. Much of it became a battleground on which proxy wars involving allied insurgencies and governments struggled for local supremacy in places like Angola, the Horn of Africa, and Chile.
Secret diplomatic efforts resulting in Nixon's 1972 visit to China altered the balance of power, as it marked the end of the notion of an unified communist front involving the USSR and China. This achievement represented the culmination of the realist approach to foreign policy that Nixon and Kissinger practiced. The opening of relations with a hostile Communist power for the purpose of outflanking the Soviet Union was the ultimate testament to the world view held by these officials.
The end of the Vietnam War and the political upheaval brought about by Watergate provided Ford scant opportunity to do much in the area of foreign affairs. His most notable effort was the signing of the Vladivostok Accords (1974), which expanded upon existing arms control agreements with the Soviet Union. Ford's preoccupation with calming the political tone of the country in the wake of Vietnam and Watergate, combined with his efforts at stemming inflation, prevented him, in the limited time he served as president, from putting his mark on U.S. foreign policy.
President Carter, attempted to radically redirect U.S. foreign policy away from the realist model advanced by his predecessors and toward a more idealistic model, with advancement of human rights at its core. While these efforts bore fruit in South America, it is less certain that they advanced U.S. interests in Europe or Asia. Congressional efforts at targeting the Soviet Union's human rights record, especially with respect to Jewish refusniks who sought to emigrate from Russia, were seemingly in line with President Carter's foreign policy, but so angered the Soviet government that, combined with the aforementioned proxy wars in the developing world, made the improvement of relations with the USSR next to impossible.
The difficulty of improving relations with the USSR was due also to that country's expanded development of strategic, or long-range, nuclear forces in contravention of the arms control agreements signed during the Nixon and Ford Administrations. Consequently, the Carter Administration's efforts at securing its own arms control treaty, the Second Strategic Arms Limitation Treaty, foundered under the weight of the Soviet record of violating the accords of earlier treaties and of its December 1979 invasion of Afghanistan.
In conclusion, the Carter Administration's foreign policy model could not sustain the weight of the realities of U.S.-Soviet relations.
I think that one way in which President Carter's foreign policy differed with Presidents Ford and Nixon was that Carter made the issue of human rights a central theme to his pursuits. President Carter was more deliberate about the issue of human rights and an intrinsic sense of good than his predecessors. In Carter's Inaugural Address, one sees how this was evident:
To be true to ourselves, we must be true to others.... The world itself is now dominated by a new spirit. People more numerous and more politically aware are craving and now demanding their place in the sun- not just for the benefit of their own physical condition, but for basic human rights.
President Carter's insistence on human rights as helping to formulate his foreign policy was a fundamental shift than the focus in the Nixon or Ford Doctrines. When President Nixon claims that the United States would not "undertake all the defense of the free nations of the world," it is a stark reminder of how much of a pivot President Carter offered. Additionally, Carter's insistence on human rights expanded the role of the United States throughout the world to intervene or comment on affairs that were deemed as human rights violations. Bringing about a potential widening of American presence, this was one area in which the Carter foreign policy differed from Presidents Ford and Nixon.