All of them are connected via common roots, namely tap, ballet, jazz music, and African-American rhythms and dance. Jazz dance originated from the African American vernacular dance of the late 1800s to the mid-1900s. An early popular "jazz dancer" was vaudeville star Joe Frisco in the 1910s.
noun. 1. a dance form or dance that is matched to the rhythms and techniques of jazz music, developed by American blacks in the early part of the 20th century. jazz dancer, noun.
This was, some say, the creation of Tap in America as a theatrical art form and American Jazz dance. Tap dancing originated with African dancers in early America. When dancing, they would articulate rhythmic patterns through chugging, scooping, brushing and shuffling movements of the feet.