Recently I've been attending classes at a strictly Ashtanga-style studio. Ashtanga is a school of yoga, and the first few classes, I didn't notice much of a difference between Ashtanga and typical “vinyasa flow". Honestly, I thought Ashtanga was just the name of the studio. Then I started to notice the subtle (and not-so-subtle) differences…
Vinyasa, joins the breath and movement together. Breath is very important and should be concentrated on more fiercely than asana positioning. Swift movement produces sweat. Sweating rejuvenates the skin and releases toxins. Ujjayi breath is utilized which, when performed with asanas, creates internal heat which purifies all humors of the body. Ashtanga vinyasa differs from most other types of vinyasa in that it is a predetermined set of asanas, rather than improvised.
Mysore, named after the Indian city in which it originated, is a marked characteristic of Ashtanga. Daily practice of Ashtanga yoga is encouraged. As a result, Mysore practice was developed. Mysore is a style in which practitioners flow with supervision, but with limited instruction, so yogis can practice at the pace of their own breath and needs. Postures are given one-by-one by the teacher, and the poses are sequential - to be followed at the practitioner's own pace. Teachers help with adjustments. Classes are typically almost silent. Less experienced Ashtanga practitioners may only practice Mysore for 20-30 minutes, while advanced practitioners practice for around 2 hours.
Emphasis on Tristhana: posture (body), breath (nervous system), and drishti (mind). Drishti concerns the fifth limb of yoga: Pratyahara. It essentially means a draining of the mind which comes through meditation or concentrating very hard. Drishti is a focused gaze, or gazing point, and is a way of withdrawing other senses by narrowing or concentrating the gaze onto sight, staring intently on one spot or non-moving object.
Body locks ('bandha') are also emphasized. This is the joining of limbs in postures. This helps facilitate Ujjayi breathing and helps gain control over your own mind. After all, yoga literally means 'yoke' or 'to join', and by binding and joining the body, maximum benefit can be expected by joining as much of the body at once as safely possible.
Mantras are further incorporated into the beginning and/or end of a class as opposed to other schools of yoga. They are written and repeated in Sanskrit. Of course, followed by an Aum. Don't worry, Savasana is customary in every type of Ashtanga.