As a ballroom dance chapter president, I am responsible to select DJ's or bands to play for our Ballroom dances -- I make all prospects aware of the music that is mandatory to play at our ballroom dances.
I use the term ballroom "dance rhythms" and typically identify the dances (waltz, foxtrot, rumba cha cha, ECS, WCS etc) that I want as primary and played more often than those I classify as secondary (samba, salsa, bachata, VWaltz, quickstep etc.)for the evening.
I was recently advised that the use of "rhythms" was not correct but that I should use the word 'dance styles' ---
Your thoughts and help
Bob Romeo

"Rhythm" has a perfectly well defined meaning. In simple terms, it's the patters of slows and quicks. I'm not quite as certain about "style," but it may refer to the character of the type of dance (for example Foxtrot and Tango may share some foot positions but if you dance them properly they look different).

Of the two terms you mention, "dance styles" may be a better terminology. Or why not just say "dances"? It all depends on what concept you are trying to convey to the bands.