What is the key difference between Woodrow Wilson's moral diplomacy and Teddy Roosevelt's big stick diplomacy?

Moral diplomacy is the name used for a form of diplomacy proposed by Woodrow Wilson.

Wilson, elected President of the United States in 1912, disliked the heavy-handed foreign policy of his predecessors. He said, "The force of America is the force of moral principle." The central idea behind his policy of "moral diplomacy" was to influence and control foreign nations and events through the exercise of economic power. In Europe, however, World War I had begun, and Wilson favored neutrality.

Under President Woodrow Wilson's "moral diplomacy" approach, William Jennings Bryan was appointed to the position of Secretary of State. Wilson also proposed an apology and compensation for U.S. actions in Panama to Colombia, but this was rejected by Congress.

Big Stick Diplomacy, a nickname coined by Roosevelt in quoting the old African proverb "Speak softly and carry a big stick, and you will go far," was the foreign policy that was later called the Roosevelt Corollary. It is an addition to the Monroe Doctrine of 1823. The Roosevelt Corollary stated that the United States had the right to enforce an "international police power" over the Western Hemisphere. It affirmed that other countries did not have the authority to cause unrest in the Western Hemisphere, most specifically in reference to conflicts between Europe and Latin America in the early 1900's.

Eventually, the phrase "Big Stick" was used to reference to any foreign policy that made negotiations with diplomatic grace, backed by the possible threat of military force.