Please excuse the definitions. They are space saving words only to avoid length explanations.  

Hatha - physical type yoga

Iyengar - detailed, precise movements

Astanga - physically demanding

Vinyasa - athletic, flowing

Kundalini - half physical, half spiritual

Yin - slow pace, seated postures held for lengthy time

Bikram - held in hot room, makes you sweat

Anusara - like hatha yoga with mind-body-spirit 

There are plenty more, perhaps you can add a few to the list