There's actually a clear difference between the two. Daydreaming is really just your mind wandering. In lucid dreaming you are clearly dreaming, but your mind is actually aware of the fact.
I've had that before. Usually when it happens is when I'm in the middle of a nightmare - then I shake myself awake before things can get much worse.
It still doesn't explain the dream you had a couple nights ago though. ...dangit you're actually catching up.
*ZSL explains Lucid Dreaming is the state when you're half awake, but alseep, and aware you are dreaming. She then explains in an easier way to say, it's the state of dreaming when you can control what you are doing*