Rumba is a dance organically related to the rumba genre of Afro-Cuban music. Throughout the history one may trace several styles of dances called "rumba".

Some dancers considered rumba the most erotic and sensual Latin dance, for its relatively slow rhythm and the hip movement. Rumba is actually the second slowest Latin dance: the spectrum runs bolero, rumba, cha-cha-cha, mambo in order of the speed of the beat.

Ballroom rumba derives its movements and music from son, just as the salsa and mambo. When son was brought to the United States it was renamed rumba. It is thought that this occurred due to the name rumba being more exotic and more marketable than Sòn.
Prohibition in the United States caused a flourishing of the relatively tolerated cabaret American rumba, as American tourists flocked to see crude sainetes (short plays) which featured racial stereotypes and generally, though not always, rumba.
American rumba is thought to have contributed to the origin of the cha-cha-cha, and indeed most figures (if not all, somehow) can be reinterpreted in cha-cha-cha.

Early American rumba
This kind of rumba was introduced into American dance salons at the beginning of the 20th century, characterized by high tempo, nearly twice as fast as the modern ballroom rumba, typical examples being the tunes The Peanut Vendor and Siboney.

Ballroom rumba
American style rumba is characterized by the Cuban hip motion or hip sway arising from the bending and straightening of the knee, as opposed to Latin hip motion stepping on a straight leg, which is used in international style rumba.
Additionally, the same move in terms of footwork often goes by a different name in American versus international.