In partnering, the lead can decide whether to perform in open, semi-closed or closed position. Dance moves or step variety strongly depend on the music (such as the rhythms played by the different instruments), setting, mood, and interpretation. Unlike salsa, bachata dance does not usually include many turn patterns.
In the West, various dancers are known to copy moves and turn patterns from various couple dances, performing these combinations in the timing used in bachata dancing, thus creating a fusion dance.
The authentic dance from the Dominican Republic in the Caribbean is a basic dance sequence in a full 8-count moving within a square. Dancers in the Western world much later made up a basic step going from side to side, and also copied dance elements from other couple dances of various origins, Latin and non Latin alike. The basic dance sequence consists of three steps and then a tap step or various forms of step syncopation (such as the “double step”). Some dancers in the west accompany the tap with an exaggerated “pop” of the hips. Bachata can be danced on the 1st beat of the musical phrase, with the tap on the 4th beat, but dancing on the 2nd, 3rd or 4th beat is also common. The tap is done on the opposite foot of the last step, while the next step is taken on the same foot as the tap. The dance direction changes after the tap or fourth step.
The original, slow style in the ’60s was danced only in closed position, like the bolero, often in close embrace. The bachata basic steps are done by moving within a small square (side, side and then tap your toes back and side, side, back) and is inspired from the bolero step but evolved to including a tap and also syncopation (steps in between the beats) depending on the dynamics of the music being played. The hand placement can vary according to the position of the dances, which can range from very close to open to completely open.
The authentic version is still danced today in the Caribbean and all over the world. It is increasingly danced to faster music, adding more footwork, simple turns and rhythmic free-styling and with alternation between close (romantic) and open position. Authentic bachata is danced with soft hip movements and a tap or syncopation (1, 2, 3, tap/syncopation). It can also be danced with or without bouncing (moving the body up on the beats and down again in between the beats by adding slight spring to ones legs). Authentic bachata was created by Dominican social dancers over the course of decades (starting around the beginning of the 1960s) and is still evolving to this day.
What is called authentic/Dominican bachata in the West is simply called bachata in the Dominican Republic and by most Dominican immigrants.
Info from the English Wikipedia. For more information see the Wikipedia: https://en.wikipedia.org/wiki/Bachata_(dance)