Ashtanga translates as "eight limbs" (ashtau≈eight, anga≈limbs/stages) that provide steps through which practitioners can progress in order to reach a state of yoga.
Vinyasa is a movement breathing system—breath movement synchronicity. The breath moves the body. It is a linking of asana to asana through the movement of the breath. With breath, core control and focus it evolves into a moving meditation.
Ashtanga Vinyasa Yoga is taught in a sequence, which is repeated every practice. The aim of the practice is to offer development and awareness of the self (“side effects” being a stronger, more flexible, toned, healthier body, are why most people are initially drawn to this practice).
Mysore is a place in India. Because it was the residence of the Ashtanga guru, Pattabhi Jois, Mysore is also a traditional method of teaching yoga that unfolds the series to each practitioner, on an individual basis, introducing new poses in increments. A beginner starts with only a few poses, gradually adding more and more as his practice develops and his proficiency and commitment evolve. Mysore classes are highly recommended for beginners, who will be closely supervised by the attending teacher. They are also suitable for advanced students and those with injuries and special needs.
In Led classes, everyone moves at the same pace, following the counts and poses as the teacher calls them out. Led classes cater to the particular mix of the students in each class.
During Self-Practice classes, students are given the space and time to develop their practice without the assistance of a teacher. What often happens is regular students that practice together may even adjust or help each other out. This class allows the student to deepen their practice without the usual distractions of practicing at home.