There are different styles of dancing Argentine Tango, some observers have identified 11 diferrent styles. Here is a quick review of the main styles.
Salon: Open or close embrace with both partners erect arose in the 1940 and 1950's where feet stay in contact with the ground and dancers are at an angle. This style is elegant, smooth, and precise, measured and allows a greater variety of movements and figures in comparison to Milonguero or Apilado. Dancers use pivots, can take large steps, and move on the dance floor.
Tango Nuevo: characterized by an open embrace with the man's hand embracing only the woman's left side and by the lifting of the feet (as opposed to the caressing of the ground in Salon or Milonguero) allows more complex moves and steps by non-dancers and
Milonguero o Apilado: A simple approach to Tango focusing on the walk, cadence, and communication between partners. It is a simple form of Tango with limited vocabulary owing to the requirement of staying in close frontal embrace. Popular or appropriate in crowded dance floors and also knows as "Tango Club" or "Tango Confiteria"
Fantasia or Show Tango: Choreographed Tango with elements of Salon, Orrillero, Tango Nuevo, as well as Ballet, and Modern Dance. This is what most people see when they see a Tango show or performance. Fantasia or Show Tango is not generall danced socially.
American Tango/International Tango: Simplified and codified versions of Tango generally not appropriate for social dancing because the movements do not follow the line of dance. These styles are not improvisational in nature and require more space than is generally available in social Argentine Tango dances or Milongas. Dancers who learn this style can generally only dance with people who know the same steps and who dance the same style.
Vals (Tango Waltz) 1,2,3
Candombe Milonga with a more pronounced African rythem or sound.
(More to follow)