Generally, the terms “Vinyasa” and “Ashtanga” are used interchangeably to refer to one breath for each movement, though in Ashtanga yoga each posture may be held for several breaths. Both styles can be physically rigorous and focus on the postures and “flowing” nature.
Core Power Yoga puts it nicely:
“Yoga authorities will probably all have a slightly different opinion on this, but what we’ve found is the terms “Ashtanga” and “Vinyasa” are generally used interchangeably, and there aren’t very many differences. Both styles of yoga are focused strongly on asana, or postures.
Ashtanga yoga translates literally as “eight-limbed yoga” and refers to the eight limbs outlined by Patanjali in the Yoga Sutras which include moral and ethical guidelines, postures, breath work, sense withdrawal, concentration and meditation. Traditional Ashtanga yoga follows the same sequence and series of poses in a precise order, and is very physically demanding!
Vinyasa or Power yoga incorporates many of the same postures, but the order or variance of the poses often changes. And most importantly, Vinyasa links breath to movement, so it’s more quickly paced and has a flowing rhythm. Vinyasa yoga is also challenging, but includes a bit more movement.”