Geographically (and as a general reference), the United States of America includes all areas considered to be under the sovereignty of the United States, but does not include leased areas.
On May 14, 1959, the U.S. Board on Geographic Names issued the following definitions, which defined the Continental United States as "the 49 States on the North American Continent and the District of Columbia..." The BGN reaffirmed these definitions on May 13, 1999.
United States: The 50 States and the District of Columbia.
Continental United States: The 49 States (including Alaska, excluding Hawaii) located on the continent of North America, and the District of Columbia.
Conterminous United States: The 48 States and the District of Columbia; that is, the United States prior to January 3, 1959 (Alaska Statehood), wholly filling an unbroken block of territory and excluding Alaska and Hawaii. Although the official reference applies the term "conterminous," many use the word "contiguous," which is almost synonymous and better known.
Learn more: U.S. Board on Geographic Names