American Rythm
American Rhythm along with American Smooth are the two categories of Ballroom Dance that constitute what is known as the American Style. Just like Latin and Standard make up the International Style of Ballroom Dance, the same goes with Rhythm and Smooth in comprising the American Style.
American Rhythm loosely corresponds to the "Latin" category of the International Style, just like American Smooth corresponds to Standard.
American Rhythm, just like American Smooth, is mostly danced in the United States and Canada, while International Style Latin and International Style Standard are danced internationally, all around the world. American Style Ballroom Dance combines elements of both traditional Latin and Ballroom dances.
The dance technique used for both International and American styles is similar, but have some distinctions of course. In addition, different sets of dance figures are usually taught for the two styles. For example, International Latin and American Rhythm have different styling, and have different dance figures in their respective syllabi.
The Rhythm dances were also influenced by American dancers of the post-WWII era, but the differences between this style and International Latin are more subtle. Costumes are similar, and while step patterns are not identical, movements are as free and explicitly sensual as in Latin.