Mr. Raduga may be busy at the moment but I am happy to answer your questions in the meantime.
1. Is there any way to tell the difference?
Lucid dreaming and OOBEs are part of the same mental phenomenon: the phase state. In such a hybrid brain state, you can perceive yourself to be somewhere other than where your sleeping body lies; and you possess waking consciousness whilst surrounded by a phantom world of the mind (no matter how much your surroundings in the phase appear to resemble the real world, it is still a virtual world of the mind.
How can one possibly differentiate between what is "in the head" and what amounts to a real separation of consciousness from the physical body when the dreaming mind can emulate any experience imaginable which includes convincing illusions such as being somewhere else? Note, also, that both what people interpret as "out-of-body experience" and "lucid dream" can give you the impression that you are somewhere other than where your physical body lies. In essence, both of them are dissociative experiences in that perceptual respect.
2. How to go from lucid dream to phase? I am not sure it is clear to me after reading your book. Is it that I should awaken from a lucid dream and then separate immediately? or can it be done from inside the lucid dream?
You can't because both are one and the same. If you are lucid dreaming, which merely means that you know you are dreaming, you are already in the phase. To me, lucid dreaming is the most advanced and pragmatic type of phase state interpretation while it's happening, because, the practitioner recognises its phantom world to originate solely in one's mind and thus entirely subjective.
The out-of-body experience describes an aspect of the phase state: the experience that one is outside of one's body (but the impression does not make it so because the brain tells porkies). If a practitioner really believes that the phantom world of the phase is outside of one's mind, or objective, then one is adopting a belief-centric stance (not dissimilar to the "astral projection" affair - this requires the belief in astral planes of existence). In my opinion, such stance is the wrong logic and can impede control of one's mental environment in the belief that this one is something entirely separate from the mind and possibly controlled by something or someone else.
So, to the second part of your question, if you suddenly realise that you are dreaming, you have just managed to enter the phase via dream consciousness, i.e. already in the phase state and therefore there is no need to return your awareness to the sleeping body in order to "separate."
This seems like the phase but appears to be a method for lucid dreaming. Is the difference that he is using his imagination rather than simply "willing" himself ?
The Phase = Lucid Dreaming; Out-of-body Experience; Astral Projection... The target is all the same. I'd say stick to The Phase guidebook. You have everything you need there.