Salon-style tango can be danced in either the close or open position, danced with an upright body posture. Salon-style is characterized by both partners staying on their own axis, and by maintaining a flexible embrace that allows for rotations of the hips of both partners. Dancers must remain aware of the line of dance at all times. Salon-style tango is usually danced to the strongly-accented beats of tango music played in 4 by 4 time.
Milonguero-style tango is usually danced in a close embrace, with a slightly leaning posture. Partners must maintain constant upper body contact throughout the entire dance, even during turns. While some instructors of the style will instruct dancers to lean against each other, others prefer that partners maintain their own balance. Dancers should lean forward only enough to remain in the embrace.
Club-style tango is a mixture of the salon and milonguero styles of tango. Club-style is danced in a close embrace, with partners loosening their embrace during turns. Club-style tango is danced with an upright posture.
The term orillero means "tango from the outskirts of the city." Orillero-style tango can be danced in either the open or close embrace, although it is mostly performed in open embrace, allowing both dancers to make steps outside of the embrace. Many people agree that orillero-style tango is one of the easiest to master.
Tango canyengue is a historical form of the dance that originated in the 1920's and 1930's. This style is danced in close embrace, with dancers typically moving with bent knees to allow for smaller steps. Body movements are exaggerated in order to accent the small steps.
Tango nuevo (new tango) developed as a style upon careful analysis of the basic structural movements of tango dancing, and the discovery of new step combinations. Tango nuevo is danced in an open, loose embrace in an upright posture, and each dancer must maintain his or her own axis. This style can be performed with either traditional tango music or more contemporary, non-tango music.
Fantasia (show tango) is danced in tango stage shows. Fantasia, which combines several different tango styles, is danced in open embrace. This style of tango is characterized by exaggerated movements and "extra" dance elements not usually associated with basic social tango. The additional movements are often taken from the dance style of ballet.
Ballroom tango developed from Argentine tango styles, but was modified to fit into the category of ballroom dancing. Ballroom tango incorporates different techniques than the smooth, Argentine dances. Tango is considered one of the easiest of the ballroom dance styles, making it a great choice for beginners. Ballroom tango is divided into two categories, American Style and International Style. Each of these styles is considered to be a social and competitive dance, but International Style is generally used more often in ballroom competitions.
Illustration from Clyde Mendes column at Salsa TV, Singapore