Slow waltz is the term applied to waltz

Waltz

The waltz is a ballroom and folk dance in time, performed primarily in closed position.- History :There are several references to a sliding or gliding dance,- a waltz, from the 16th century including the representations of the printer H.S. Beheim...

 in countries where Viennese Waltz

Viennese Waltz

Viennese Waltz is the genre of a ballroom dance. At least three different meanings are recognized. In the historically first sense, the name may refer to several versions of the waltz, including the earliest waltzes done in ballroom dancing, danced to the music of Viennese Waltz.What is now called...

 is the form of waltz commonly practiced. Some confusion occurs when dancers come from these countries to places like the United States

United States

The United States of America is a federal constitutional republic comprising fifty states and a federal district...

 where "waltz" events and invitations are not what they might expect.

Slow Waltz was also the name of a dance in the International Standard dance category of ballroom dance

Ballroom dance

Ballroom dance refers to a set of partner dances, which are enjoyed both socially and competitively around the world. Because of its performance and entertainment aspects, ballroom dance is also widely enjoyed on stage, film, and television....

s. Now it is officially called simply "Waltz

Waltz (International Standard)

Waltz is one of the five dances in the Standard category of the International Style ballroom dances. It was previously referred to as Slow Waltz or English Waltz....

", but "Slow Waltz" is still in the informal use, to distinguish from other types of waltzes.