Maybe Ashtanga yoga is like yoghurt fermentation. When you add a bit of leavening agent to the milk, in which the bacteria are located, they convert milk into yoghurt. No matter in which country you blend your leavening agent with milk, the same events will always happen. But the yoghurt will taste a bit different every time. The leavening agent is the same, but the milk changes. Likewise, Ashtanga yoga has a different flavor all over the world, but it is still remains Ashtanga yoga.
If you have ever learned the Vinyasa system, you can walk in and practice with Ashtanga shalas all over the world. This is a beautiful experience, and feels a bit like being at home anywhere the world. In addition, you will notice small differences that might be valuable details for you and your practice. This universality of Ashtanga, combined with the individual characteristics of teachers and students, is part of the special magic of Ashtanga.
Many new ways of yoga in the West originated from, and were inspired by, Ashtanga Yoga. With these, the traditional form of Ashtanga was lost, but the basic principle, unity of movement and breathing, stayed preserved. This principle is called Vinyasa. Therefore, one can also combine these children of Ashtanga as Vinyasa yoga.
The following styles form part of Vinyasa Yoga - its founders have all learned from Pattabhi Jois: Prana Flow Yoga by Shiva Rea, Jivamukti Yoga by Sharon Gannon and David Life, Power Yoga by Bryan Kest, Dynamic Yoga by Godfried Devereux, It's Yoga by Larry Schulz.