What is the difference between vinyasa, Anusara, Iyengar, and Ashtanga, kundalini, and hatha yoga?

Yoga is a practice including meditation, selfless service, devotion, study of truth, and much more.  One branch of this practice is  hatha yoga, which involves the physical body and breath.  Many styles of hatha yoga have been developed in modern times, and they are all based on similar movements and exercises, with a different approach. 

 Vinyasa and ashtanga are more flowing practices, choreographed like a dance, you will move through one posture after another in sequence, and often return to a pattern, or "vinyasa."  Iyengar yoga is based on the teachings of B.K.S. Iyengar, an Indian yogi, and this style is very grounded in technique, specific alignment and strength building.  Anusara yoga was created by John Friend, and ties the practice into nature using metaphors and imagery.  The alignment system used by John Friend is similar to Iyengar's, but more fluid.  This practice embraces other styles.  Bikram Yoga is a sequence of 26 postures practiced in a hot room, like a sauna.

Many teachers have experience with a variety of style, and find their own way of teaching the practice of hatha yoga.