Yoga is a Sanskrit word, which means union. It is much broader and deeper than doing physical asanas. The asanas is just the tip of iceberg :) As you said, when you practice the asanas, your body and breath becomes more controlled. The next level is you control your thoughts - and not vice versa -> union of body, breath and mind. As you become more serene, your meditation starts getting deeper -> union of mind, body, breath and self.

I came across this video recently, where three "genuine" yoga teachers are asking questions about yoga and meditation. The format is initial 10-12 minutes, the yoga teachers talk about their experiences, and then in rest of the video, they ask questions to Sri Sri Ravishankar about deepening mediation with yoga: https://www.youtube.com/watch?v=a7HEmsY29EU