How did the foreign policy initiatives of the george w. bush administration depart from the policies of other presidents since world war ii?

A key difference was in using US military power preemptively to combat enemies of democracy around the world.

The "Bush Doctrine" in foreign policy had these core ideas:  that the United States could pursue this goals on its own (without need for United Nations partnerships), that preemptive strikes were allowable against countries that harbored terrorists, and that regime change for the sake of promoting democracy was a good strategy.  

Applied in regard to "the war on terror," Bush's foreign policy advocated that the best defense against terrorism in the world was to use American power to spread democratic values in countries that were potential breeding grounds for terrorist activity.  This sort of policy agenda was part of the "neoconservative" view of a number of  President George W. Bush's advisers -- especially some who had also served in the administration of his father, President George H.W. Bush.  In the wake of the 9/11 attacks, there was a desire to push American values and not be shy about doing so with the use of American military might.