Theodore Roosevelt's foreign policy was commonly known as "Big Stick Diplomacy," based on his favorite expression to "speak softly and carry a big stick." While his actions in Colombia were somewhat questionable, he did promote U.S. foreign interests in other ways, including sending the U.S. Navy on a tour around the world, the so called "Great White Fleet." His foreign policy was in keeping with his personality, as he was fond of a good scrap from time to time. As Under-Secretary of the Navy under President McKinley, he had ordered Admiral Perry to steam to Manila Harbor after his boss left for work, hoping to engage Spain there. He was always disappointed when war was avoided, even attempting to volunteer to fight in World War I. He was turned down because of his age.
Woodrow Wilson's foreign policy was often denominated "Missionary Diplomacy," as he tended to pursue matters more from a matter of principle than policy. He was idealistic, but at the same time could be stubborn. He sent Gen. John Pershing to Mexico in a failed attempt to capture Pancho Villa; he also interfered in a coup taking place in Mexico. At one point he sent American troops to Verz Cruz, Mexico, making the remark that:
I suppose there is nothing for it but to go down there and take the bull by the horns.
Wilson was somewhat idealistic at the Versailles Peace Conference, but again could be stubborn. He had a young Ho Chi Minh thrown out of the conference when the latter asked for self determination of the people of Indochina. He was not so forceful about the entire Fourteen Points as he was about the League of Nations. When Congress proposed changes to the League covenant, Wilson steadfastly refused to consider them. In the end, the Treaty was not ratified because Wilson would not budge.
The major difference between these two presidents' foreign policies is that President Wilson tried more to be idealistic while President Roosevelt was known for being much more interested in advancing the interests of the United States, regardless of what was "right". For example, Roosevelt was willing to infringe on Colombian sovereignty and to engage in fairly shady dealings to obtain the right to build the Panama Canal. By contrast, Wilson tried to pursue a much more idealistic approach. This is seen most clearly in his attempt to push the Fourteen Points at the peace conference that followed WWI.