what I call "Real Yoga" is meditation. The problem is it is hard to find that today especially within cities. These people are on the top of a hill before the sun rises and wait for it. They take ice cold showers in the morning, and study a lot of old astrology, alchemy etc...each position is almost like a prayer or mental state that you need to be in. Breathing in a certain way during each position is mastered too.
If you are paying for a yoga class in a studio, its more of stretching exercises.
This can also apply to Tai Chi. From an instructor i know, You are supposed to adjust your breathing and mental focus to parts of the body with the vision of something going through them.
I havent meditated in so long but used to do it 2-3 times a day. I even used it instead of sleeping on rare occasions. It is something that through my experience has worked and I have just been too busy to do it as often as I would like. Those who are interested, I would say go for it, and don't trip off the "different types". You can meditate while walking, drawing, sitting, laying down, cooking. The idea is to just calm your mind and have a consistent breathing pattern.
sorry for the long post. Who ever read it all.