Answer:
there are two main categories that ballroom dance is divided into: Ballroom/standard and Latin American. Ballroom/Standard has five dances within its category that are the Waltz, Foxtrot, Quickstep, Tango and the Viennesse Waltz, the Latin American category also has five dances that are the Cha Cha, Rumba, Samba Paso Doble and the Jive (the Jive is why its Latin AMERICAN, not just Latin) theres other dances known as sequence dances that are in two categories as well, New Vogue and Old Time/Classical Sequence. in these groups i cannot remember how many dances are in each, nor am I going to attempt to name them but what makes them different is that all the dancers have the one routine, there is no variation on it and they are judged in copetitions by floor prescence, footwork, posture etc.
Hope i helped.