I've been doing some research on Hinduism.
From what I've read, the term "Yoga" has two different meanings within the context of Hinduism. One is basically a sect (I've seen the term "school" used) of Hinduism. The other is a set of postures, positions, etc. used by that sect/school. Confused? So am I.
From what I understand, the Yoga that a lot of people practice is simply used as an exercise to improve flexibility, etc. and isn't intended as a religious practice, Hindu or otherwise.
I've read that many Balinese practice some form of Hinduism, thus it isn't really accurate to say it is an Indian religion. It may have specifically Indian FORMS though.
I wouldn't get very far with Yoga as an exercise right now. My flexibility is HORRIBLE.