If you are lucid you know you are dreaming. But if you dream this and not actually realise that you realised this IN a dream rather you just accepted it as a reality and therefore you perform the thing you would want to do in a lucid dream but experience the same feelings as a real lucid dream.
Yes, it is fully possible to ‘think’ that you are lucid, and do lucid stuff in dreams, without being lucid in the definition of that you know you’re dreaming. As I can remember, we have discussed about it before on this forum, so it’s not unknown to us
I’ve have something a bit like that quite often, not quite like you explained, but pretty much the same. What happens is I control everything in my dream, just like a LD, but I don’t actually know I’m dreaming.