Yoga is actually a philosophy. The Bhagavad-Gita mentions four types of yoga, which I think are karma, bhakti, jnana, and raja Yoga. It also talks about ashtanga Yoga, which has a new definition today.

However I think a Upanishad or other text also classifies various types of Yoga. I wonder what all the classifications are then.

I was surprised that some Theosophists--maybe even HPB--call hatha Yoga black magic. Actually maybe it was just some new AAB-influenced thinkers. I was into Yoga before Theosophy and that just sounds nonsensical to me. Maybe 'dugpas' use hatha Yoga for the wrong reasons because it is physical Yoga, but there is nothing wrong with doing exercise. In fact the Shaolin monks thought you should exercise to meditate better, and hatha Yoga is suited to making it easier to formally meditate in sitting or other positions. Modern Ashtanga Yoga also does the same thing to a greate by 'correcting the alignment of the body.'