This implies there is a self and then a "true self", which is somehow different from the former.
The only thing different is our perceptions. If we are locked in the egoic self, it is the set of eyes we look out through and reflect upon ourselves with. It sees only through that set of eyes. If we are able perceive with the eyes beyond that, then we are not locked in the egoic self, but recognize our true Face, which includes, but is not limited to the egoic self. You are correct that the ego self is not "other" to the Self, but how we perceive it from the ego self sees Self as other, as long as the eyes of the egoic self are the only ones we understand and are operating out of.
A simple analogy is to understand how a child when asked to point to himself will point to his body an exclaim, "This is me!". But if you as the same question of a teen they will point to the things they like, the friends they have, and a list of ideas. They may point to their head, their mind and say "This is me". The more consciousness self-aware, the more inclusive. They realize their body is not "other" to themselves, but the seat, the locus of their self-identity transcends but includes the body. Their center of gravity shifts from the body as the child understood "me" to be, to their minds, their ego-self they now self-identify with and as.
To know and to shift the center of gravity from the ego-self to Self, does not make ego-self or body-self other to it either. But when you are living only in the ego, the Self is perceived as other, and yourself other to it. It is unknown to you, asleep as it were, or "hidden" from the self that is actively and exclusively identifying with only the ego-mind. Once awakened, then we see it is none other that who we have been all along. But not before then.
Here is my take on this -
I am real now. When this is so, what is there to realize again? The only realization then can be that there is nothing new or hidden to be found. This knowledge will stop one from searching.
And this is very true. But you are aware that you are in fact seeking in a sense? I'm fully in agreement that we need to stop looking for it as though it is something other to us. The real key is to "seek to not seek". The effort to find it, it to make an effort to make no effort. And so forth. To be searching for it is to looking outside yourself to find your own eyes. "Where are they," cries the person looking everywhere outside himself for his own eyes which are the ones he's looking through to find themselves. The seeker seeking to find needs to not seek to find, but seek to realize. Realization is a much better word because it is the "ah hah" moment of awakening to what has always already been what and who we have been all along.
But to "not seek" in the sense of being purely apathetic, turning on the TV and drinking beer without an eye to anything but comfort and security will not result in awakening to Self. But seeking to not seek, learning how to simply allow what is to be realized by a deliberate action of opening oneself to one's Self will. Actually, to me the "not seeking" you describe comes later, once we have exhausted all our Atman projects, all our substitute for that actual Realization. It comes at the end of all our efforts to "attain". Another reason I rebuff at the use of "attain", or "achieve" in regards to Enlightenment. One does not attain their own eyes, or achieve their lungs. You simply realize that the one sought after is the one seeking, and you rest it that, as that.
I really think we are saying the same thing, and this is more an exercise in finding language than any real conceptual difference.