This is what I take away from this thread.

False Lucid is a regular dream, in which a dreamer dreams about being lucid. But he doesn't gain lucidity. Awareness.

And lucid dreams can be of different quality. Stable or not stable, foggy or sharp and focused, realistic or not so much, and we can have different awareness. We can remember our whole Waking life, or not even our next lucid dreaming goal.

And for a novice lucid dreamer, it really shouldn't matter. The goal is to achieve a LD through practicing awareness and getting better at memorizing things, plus RCs and mantras and other things. And after a few lucids, when it's clear that we can do it and our confidence is up, we can work on making our lucids of better quality.