Where do all the distinct yoga types come from ?

There's 1 variant of Yoga, the Hatha-Yoga, which has developed a couple of various approaches in practicing it. Even though Hatha Yoga is very old, the most alterations and variants of it have come out in the last years. There are many different methods to exercise it, but i want to mention the greatest known ones: Shri Krishnamacharya developed together with his student, a extremely popular variant of Hatha yoga. It is known as viniyoga. The Hatha Yoga that is teached in the previous decades is mainly influenced by BKS Iyengar, K. Jois and Devi Patabhi.

Viniyoga is based on a "follow-up process" (vinyasa krama). You shouldn't just do static trainings. It is more than that. The aim is always to focus on the diverse abilities every individual student has. Controlled breathing is an essential aspect of Viniyoga. The breathing techiques require a special position.BKS Iyengar, he is a relative of Shri Krishnamacharya and TKV Desikachar's uncle, invented Iyengar Yoga - another form of hatha yoga. It got truly famous in the western countries. Iyengar Yoga uses tools like cushions, ropes and other things in cooperation while using typical movements. The developer of Iyengar Yoga built an Yoga institute in Pune (India), which now is managed by his wife.

Ashtanga yoga was founded by K. Pattabhi Jois, who was born in 1916. With his modern views he represents, he also attracts Western students in his Ashtanga Yoga Institute in Mysore (India). The Ashtanga Yoga is also very well known as "Power Yoga".
"Power Yoga" is a variation that is based on a hard workout. Although it is theoretically based on the eightfold path of Patanjali, Ashtanga yoga doesn't differ in a lot of aspects. An additional good known variation may be the Kripalu Yoga which build up on the 3 stage strategy. It is, like the other variations mentioned, adjustet for the western population. It starts with practicing on how you breath and move your body. The great thing is to just practice the positions for a short time. In the second stage following the exercise of the various positions there shall also be meditation. The meditation will take a longer time then the techiques you use in the initial stage. At the end you have to accomplish your meditation on the go.

Additional Ressources:
How to begin with yoga
How to begin with yoga
The most popular variations of the Hatha-Yoga