Argentine Tango Styles of Dance
Y ou could say there are as many Argentine Tango styles as there are great dancers from the old days. On the other hand you can describe some categories of similar styles. This discussion is of course simplified.
First, we can classify tango by context: Stage, Social Dance (Milonga), or Practice.
Stage tango is flamboyant and dramatic, usually choreographed, and technically perfected to a high level for an audience. A Social Dance has specific codes of behavior, common sense things, for the most part, such as avoiding collisions with other dancers, walking the lady back to her seat, dancing musically instead of showing off, and taking care with your partner. A practice is an informal setting where you can practice things more casually.
Second, we can categorize by open or close embrace.
In fact, all tango is danced close, so "Open Embrace" means variable embrace: stay close while walking; open up when you need room for the follower's hips to pivot. "Close Embrace" means dancing close all the time. Another, more technical distinction is whether the ochos pivot before or after the leg passes. Saying the same thing in reverse, whether the "floating leg" normally passes before the pivot (close-embrace), or after the pivot (open embrace).
Third, we can look at historical styles of tango.
Ballroom tango dates from the earlier, more vintage style of tango of the early 1900s that arrived in Paris, crossed the Atlantic with Irene and Vernon Castle, and became stylized by the British for performance competitions.
Aside from Ballroom, today's Argentine Tango styles all date from the Golden Age of the 1930s and 1940s. This is the period when a number of typical elements of tango developed and solidified, specifically the lady's cross and the turn with sacadas. While it seems like every neighborhood of Buenos Aires in the 1930s to 1940s had its own tango style, most dancers who have learned in the past 20 years borrow bits and pieces from all these neighborhoods and eras.
Fourth, we have various labels or names of styles used with greater or lessor accuracy.
Salon tango in Argentina generally means "social tango". Outside Argentina it is used as a name for an "Open Embrace" (variable embrace) style of,tango with smooth, walking steps, frequent use of the tango turn or giro with sacadas, and occasional use of fancier elements.
Milonguero tango refers to a very-close style utilizing plenty of check-steps, appropriate for crowded dance floors. The woman does less pivoting in the ocho, and her hips do not turn side-on to the leader.
Fantasy tango is just another name for stage or performance tango, utilizing plenty of stylized kicks (ganchos and boleos), fancy leader's moves, and even lifts and the acting out of short vignettes, some of which are classic or tacky as you wish: the classic pimp & whore, the barroom brawl, the passionate encounter under the street lamp, etc...
Nuevo tango is a term often used for a current style of tango that developed from the analysis of several skillful dancers who trained together in the 1990s in Buenos Aires (Gustavo Naveira & Fabian Salas, among others.). This style, or as I prefer "analysis", is built on a balance between the leader's and follower's axes, and an exploration of ultimate possibilities: if we can do a move on the left, what happens if we try the same move on the right? If the leader does a move, is it possible for the follower to borrow a similar move? What modifications do we need to make in order to deal with the asymmetry due to the embrace or the lead-follow relationship?
In addition, some people use Nuevo to include new vocabulary, some of it borrowed from other dance forms like swing.