What is the differences between Homido Virtual Reality Headset and Homido Headset + Bluetooth gamepad bundle? Which one of these two do I have to buy to enjoy games and video on my smart phone?

The difference between Homido and Virtual Reality Headset and Homido Headset is none, as they are intertwined to work together. The Bluetooth gamepad is designed for you to control video games or movies that you are viewing with the Homido device. I'd go with the second option, if you'd like an extra controls, but it's not necessary, as the controls will be with your fingers before beginning a game or after, so that you may turn it off. Additionally, your right and left head movements is what controls most games on any of the Apple, Google Play and other stores.