In English ego is associated with Freud's name for the area of consciousness we usually inhabit in the world, navigating the space between raw impulses and moral abstraction. This kind of schism between different kinds of consciousness is not exclusive to Freud, and moreover I think it's at the heart of the question you raise. (On a side note, it seems it would be Freud's Id, not Ego, that would be the childish, greedy part of oneself.)
Another portrayal of split consciousness is Stirner's. He is interested in illuminating a split between the self-aware one who sees themself as the creative/destructive center of their world, and the one who is duped by abstractions. As you mentioned, there are similarities between Stirner and Laozi in terms of awareness and delusion. Going out on that limb, I'd say there are actual significant (if not substantial) similarities between Stirner's "ego" (though I seem to remember that the term he used means something more like "uniqueness" or "ownness", not that "ownness" is a real word or anything) and Laozi's Tao (which admittedly I know nothing about). Namely, it seems both are described as nameless, which is no small matter to my mind.
Now if we accept the namelessness of the namelessness which Stirner's ego and Laozi's Tao are meant (?) to name, then perhaps we should call into question your line of questioning. How can I tell you "what exactly" something ineffable is? If it is your uniqueness, or way, or whatever, I very much doubt anyone can tell you what it is. If one wants to go "into the unknown," it seems a mistake to get caught up on concepts like the Ego, the One, or the Way which were meant to be signposts.
I'm not the one to expand on this topic, but I'm almost sure I read somewhere that Stirner was inspired by Taoism. So there may be hope yet.