The defining feature of Vinyasa is the alignment of movement and breath; and, technically, Ashtanga is a form of Vinyasa. Both styles focus on combining breath and movement.
The biggest difference between Ashtanga and Vinyasa lies in the sequencing. Ashtanga Yoga consists of three series of postures: primary, secondary, and four advanced series. A practitioner must master one before he or she can move on to the next. Each series consists of a predefined order of postures (asanas) that students practice the same way, every time. Vinyasa class sequences vary, and the practitioner might experience an entirely different sequence each time he/she practices.
As Ashtanga class progresses, the postures in the series, become more complex. Vinyasa Yoga sequences, on the other hand, often feature a peak pose. The peak pose is a challenging and complex pose selected for a particular practice. The teacher leads the class through a sequence of postures that helps students prepare for practice and recover from the peak pose.
Both Ashtanga and Vinyasa employ a three-pose transition, called a “Vinyasa,” which includes Chatturanga, Upward-Facing Dog, and Downward-Facing Dog. In Ashtanga, the student performs an asymmetrical pose on the right side, moves through a Vinyasa, and then repeats the pose on the left side. In Vinyasa Yoga, a student may link several asymmetrical poses together before performing the Vinyasa and switching to the other leg.
Finally, students of Ashtanga Yoga do not use props, posture modifications, or music. In Vinyasa classes, some teachers allow props, sometimes use background music, and encourage their students to modify postures if needed.