The original Waltz music is fast, and the dance which began in Vienna, Austria would be called the Viennese Waltz - no surprise. The following video clip shows the Viennese Waltz danced beautifully. These are the only steps which people tend to dance socially & the only ones in the sylabus up to 3rd Gold Star medal (ISTD) (or Gold Bar IDTA).
The clip below show the Hiltons performing a fabulous choreographed Viennese Waltz which would not be possible to dance entirely using lead/follow technique alone.
The American Country Western Dancers also dance the Slow Waltz. The rhythm is still waltz, but the character has changed due to the music so the clothes match that genre.