Hey there, welcome to DV! I hope that you enjoy your time spent on the forums.

To answer your question about dream control: lucidity does not mean that you are controlling the dream, it just means that you're conscious you are dreaming. Similarly, just because you control your dream does not mean that you are lucid. Dreams can trick you into thinking that you have some sort of god-like power and that's how you can (for example) fly, and so you control where you fly at but you're not necessarily lucid.

But is there a "half-lucid" state? You can say that the rule is that if the dream world doesn't come in clearly and vividly once you realize you are dreaming then you are only half-lucid, or partially lucid, but lucid nonetheless.

Enjoy your time here!