Rhythm Tap-- also called "Hoofin" or "Buck Tap" -- is where the rhythms the feet make are the most important element. It's really using the feet as an instrument. Arms are loose and casual. Famous Rhythm Tappers: "TAP DOGS" or Savion Glover.
Jazz Tap is a light style where the dancers use classical jazz music. Famous Jazz Tappers: Brenda Bufalino, Sam Weber, Manhattan Tap Orchestra, and the Jazz Tap Ensemble
Charleston Tap is an old, energetic, pop style of tap.
Flash Tap is usually a "Buck Style" dance filled with lots of tricks. Famous Flash Tappers: the Nicholas Brothers.
Soft Shoe is a soft, lyrical style often done without taps on the shoes.
Waltz Clog is done in 3/4 time. It originated with the Irish and was done often around the turn of the past century. Famous Waltz Cloggers: Pat Rooney and many old Vaudeville acts.
Broadway or Rockette Style Tap is often seen in musical comedies and includes lots of arm style and high kicks. Famous Broadway-style Tappers: Ann Miller, Eleanor Powell, and The Rockettes
Balletic Tap is a form of tap done to classical music with grace and style. Famous Balletic Tappers: Fred Astaire and Paul Draper.