Hey everybody, first post (I hope I don't screw up with all the rules).
Obviously this question works under the premise that the United States can be defined as an Empire (considering continental aquisition of land and overseas expeditions like the philippine colony). I would like to know if other empires defined themselves differently, or more openly as an "empire"? Probably the contemporary rivals e.g. Britain, Germany, France, Japan, Russia
This can be split between three factors.
First, America used to be a colony itself, so Americans were far less likely to be pro-colonialism in the way the Great Powers of Europe were. Even the most aggressively colonial Presidency in American history sold its colonial ventures on traditional American humanitarian values and explicitly disclaimed any desire to acquire new territory. This is also reflected in the American approach to colonial control in the territories taken from Spain at the end of the Spanish-American War. At the end of the war, Cuba was reduced to de facto protectorate status, and Puerto Rico, the Philippines and Guam were taken under direct American control, but were later given a modicum of self-government. By modern standards, that would've been an atrocious breach of international law; by the standards of the late 19th century, it was rather good behavior for a Great Power.
Second, the Americans realized very early that their control over foreign colonies that permanent colonial domination was untenable. By the Jones Act of 1916, it became the official policy of the U.S. government to grant the Philippines independence at an unspecified later date-- and by 1934, the Tydings-McDuffie Act agreed that the Filipinos would get independence in 1946. Similarly, Puerto Rico was granted limited self-government in 1917. A Tydings-McDuffie-style independence process was mooted for Puerto Rico in the 1930s, but was defeated because of Puerto Rican Liberal Party opposition.
This is very different from the hubris of Britain, France, and the other Great Powers, who assumed that the metropole could maintain its primacy forever. This, in turn, led to the hasty, bloody, and incompetent decolonization waves of the post-war era. In Africa, especially, local elites had never been groomed to govern, leading to the proliferation of "one man, one vote, one time" autocracy.
Third, of course, America had less of a need for overseas colonies than France, Britain and Germany. There was an entire sparsely-populated continent that Americans could settle and exploit for raw materials during the late 19th century. The Americans could simply sweep aside Indian resistance by force, and on Indian land build mines, cities and farms. (A similar process occurred in Russia, during the settlement of Siberia.)