The embodied self, which not a distinct thing but a highly coherent set of overlapping matters, is a factor that the mind must include in all its calculations, it is a player, an important stake-holder, among the most important ones, you might say. Consciousness, on the other hand, is nothing of the kind. For a start it tend to foster the illusion that it is the mind, or rather the mind is no more than it - this is patently false, but the mind doesn't seem to care enough to disabuse it. Perhaps only in dreams does the mind demonstrate some unease about its belated parasite. This is far from the whole story. The consciousness present in others matters very much, and your own consciousness too, in so far as it is the concern of others, which turns out to be quite a bit. For all the tremulous privacy of consciousness you might venture the idea that it only 'exists' due to your uncertainty about others and how they, as minds, interpret you.