Virtually all ballroom training in the US is provided by private businesses. There is very little training in public schools.
Dance schools in the US are divided into two types: franchise and independent. The largest franchises are Arthur Murray and Fred Astaire. Generally, franchise studios allow only their own instructors to teach in their studios and have their own styles and competitions.
Independent schools are usually owned locally and are run by a teacher (although some are owned by financially successful amateurs). Some independents use only their own instructors but most allow independent teachers to use their floors for a fee.
Most Americans learn the American style of the basic roster of dances. We call American waltz, tango, Fox trot, and Viennese waltz Smooth dances and rumba, cha cha, and swing Rhythmic dances. Rhythmic also includes Mambo and Bolero.
Many Americans also practice what we call International style but what the rest of the planet just calls ballroom. The folks who study International styles usually do so for competition.
There are also other styles which are very popular is the US: salsa, hustle, merengue, samba (American style), and several others. Also very popular are what are called "country and western" styles such as west coast swing and two step.
Quickstep is not in the American roster but has become more popular thanks to television shows.
Most social dancing is done at studio parties but some nightclubs also provide dance floors. Local associations also sponsor dances at local venues with dance floors.
There are numerous private associations involved with ballroom in the US. The major ones are the NDCA (National Dance Council of America - actually a governing body for several other associations) and USADance. USADance used to be the governing body for amateur dancing exclusively but has taken on other roles in recent years.
USADance is comprised of local "chapters" which provide some dance-related services at the local level. USADance also sponsors a few regional and national competitions.
There is also the US version of Britain's ISTD (Imperial Society of Teachers of Dancing).
Others on this board can provide you with additional details.
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