Jazz dance has Fosse, Simonson ( the only two I know of) and I sure many more styles
Modern has Horton, Graham, Limon.
Ballet has Vaganova, Cecchetti, Russian, Danish, English styles, to just name a few.
Yoga has Vipassana, Hatha, Jivamukti, Svaroopa, Ashtanga, Bikram and…
Say Jazz, modern, ballet, or yoga and most people will have some idea of what you are talking about. Might not be exactly what you mean, but in the ballparl
Contact Improvisation, as of know, has one name. Yes, there are regional styles – West Coast, East Coast, European. But as CI is so young compared to the other movement modalities mentioned (how old is Yoga?!?), it has not been around long enough to change and become codified.
Eventually Contact Improvisation will become codified and that is just as good as it is bad. Codification can lead to clarity, but also to ossification. Codification can then also let practitioners of the form reject was has come before and discover new ground within a form. If CI does not expand and grow (some people might see this as becoming something else and the death of the form) it will stagnate.
I look forward to how many styles and flavors of CI there will be in another 38 years.