The reign of the "Imperial Presidents"—Theodore Roosevelt, William Howard Taft, and Woodrow Wilson—was an intriguing era of the United States presidency. As their collective nickname suggests, these presidents were heavily involved in foreign affairs, but they had different approaches that reflected their different definitions of freedom.
Roosevelt was a bullish Republican and foreman of the Progressive Era zeitgeist. His strong, forward demeanor, coupled with military education and experience, resulted in a foreign policy that mirrored his ideal of freedom: "Big Stick Diplomacy." Roosevelt believed that freedom entailed active participation in preserving such, and his presidential foreign policy did just that. Even though a big part of Big Stick Diplomacy was the visual display of potential force to discourage actual military action, the flaunting of such power (globally parading the Great White Fleet, for example) was an active effort to maintain freedom.
Taft was hand-picked by Roosevelt to succeed him; however, Taft lacked the boldness of Roosevelt. Roosevelt found Taft to be soft, and the Progressive Republicans derided him for abandoning the progressive agenda and yielding to special interests—he was seen as easily bought. Corroborating that style, Taft termed his own foreign policy as "Dollar Diplomacy." He used the United States' growing economic prowess to its advantage on the global scale. He urged Wall Street to invest in Latin American economies and supported revolutionary causes that furthered his financial agenda. Taft believed that freedom could be bought and maintained through national economic might.
The 1912 election was a bitter spectacle between three frontrunners who all served the presidential office. Roosevelt, dissatisfied with his successor, challenged Taft for his reelection nod from the Republican Party. When Taft won, Roosevelt formed his own party, splitting the Republican vote and allowing Wilson, a Democrat, to win the election.
Wilson was more concerned about the political structures of Latin America, involving himself (or not) in relation to how the resulting politics would benefit American interests in the long-term (he accused his predecessors of looking to benefit only in the short-term). His strategy was known as "Moral Diplomacy." As part of his "New Freedom" campaign platform, one major issue Wilson addressed was repealing high tariffs put in place by his predecessors. By doing so, the US gained favor with trading partners. He also repealed the act that made American vessels exempt from paying the tax to use the Panama Canal, which pleased nations like the United Kingdom. Wilson believed freedom was maintained by currying favor on the world stage through fair and moral political behavior.
Through these three presidents' administrations, the United States certainly asserted itself on the world stage—militarily, economically, and politically. All three presidents had a running theme of promoting "American exceptionalism." All three had great interest in Latin America and how it would affect the US, and all three were concerned with American power, global standing, and freedom. Their definitions of freedom may not have varied much, but their methods of protecting it did.