Hi @alexopenyoga and @saramiller. Just to clarify there is only one type of Ashtanga Yoga and that's Patanjali's 8 branched yogic system. What Sri. K.Pattabhi Jois and Sri. T.Krishnamacharya did was take those teachings and apply them from the filosofic aproach into a more hands on aproach. Yama and Niyama are supposed to be practiced by anyone, period. From there asana is practiced through posture, pranayama through breath awareness to how exact is your vinyasa (movement and breath linkage) and pratyahara through drsti or the gaze points. All other four branches according to Patanjali can't be practiced. They will manifest on their own as a result of the practice of the previous 4 branches. So pratyahara comes from the practice of asana and pranayama, dharana comes from the cultivation of pratyahara. Then when scence abstraction is something you don't even have to think of but it just manifests once you start practicing, then dharana will come. A single pointed concentration, from which dhyana or meditation, a longer period of time in dharana will manifest. Finally if enough dhyana is cultivated you will forever be in that dhyana state, which is samadi.

Now off to the styles of Ashtanga Yoga as an asana practice, there is only one method and that is Pattabhi Jois method.

Ashtanga Yoga is taught in Mysore India at my school the KPJAYI - Krishna Pattabhi Jois Ashtanga Yoga Institute and the method there is self practice or what is popularly called in the west as "Mysore Style" where you practice your own portion of the series you are on until you make is perfectly clean and then you are "given" another posture to work on so on and so on. This is the original way of teaching Ashtanga Yoga.

When Pattabhi Jois came to the west he found himself in front of hundreds of students who wanted to be taught. He saw he couldn't teach Mysore Style to all of them, so he invented guided classes. Yeah we all are in debt to Sri. K.Pattabhi Jois, not only for bringing Ashtanga method, and all other vinyasa styles that spawned out of it, but also for inventing the led class. I don't know if it was his invention, but he surely was the first one to use it in the Ashtanga Yoga world.

Now diferences between the use of Ashtanga Yoga and Ashtanga Vinyasa Yoga. Well Ashtanga Yoga is Patanjali's 8th limbed Yoga System, with an asana practice as a 3rd branch. Any asana practice. Ashtanga Vinyasa Yoga is the Vinyasa Yoga style adopted and molded by Sri. K.Pattabhi Jois from what his teacher T. Krishnamacharya taught him.

I hope this helps clarify and if you have any questions, just let me know. I'm always open for a good yogic talk.

Namaskar.