The relative aspect of self is just a self-organizing narrative that allows us to function in the world. Also, often known as the egoic-self, where there can be healthier and less-healthier forms of this.
The existentialists would take this one step further by claiming to break the grip of the past by aligning with the choices we make going forward. But this version of self is just replacing one story about oneself with maybe a better story. But our locus of identity is still mostly organized around concepts of our self-conscious doer, albeit with a sense of more autonomy than disposition.
Going a step further, the not-self teaching (anattā/anātman) in Buddhism would claim all concepts about the self are false and that this can be Realized by the practices of emptiness. But there are some misunderstandings here also, as the original teachings did not claim there was no self but where the self was-not.
The Buddha never denied a self, but that there was no self to be found in the five aggregates: namely translated as corporeality, feeling, perception, volitional formations, and individual consciousness. Yet, ātman remains. The ātman was not impermanent, unlike the aggregates (skandhas) which comprised of a false self.
Still, ātman is seen as universal, which leaves little to room for the particularities around individuality. It would seem to me even Self-Realized persons still act as persons, with particular dispositions, inclinations, and personalities. These are the constraints and gifts that make us human, even as a liberated one. So Buddhism does not definitively speak of finding the true self, but only losing the false one.
By contrast, Christianity revolves around the notion of the Person which is derived from the doctrine of the Trinity. As a Person, we are substance-in-relation.
The First relation is vertical in sharing in the Infinite. We are receptive of “one’s own existence from a Source that remains ever transcendent.”
“Being in a state of grace is the Christian version of what the Buddhist calls the primordial state or essence of mind. It is not passive in the sense of being merely inert, but actively receptive to whatever comes from the Infinite.”
We are not just Consciousness, but we possess consciousness. Therefore, we possess an “inner unity that transcends the flux into which Buddhism would dissolve us—a flux of physical and psychical elements, of individual moments in time generated one after another by karma.”
The Second relation is horizontal in sharing with others in the world. This makes this inner unity paradoxical. Our true center is not just in ourselves, but also outside ourselves. We exist in relationship to others. Therefore, we can’t find our true self just by introspection. Again, we are substance-in-relation!
If we look to the image of the cross, we can symbolically find a paradoxical and Trinitarian true self at its center. This center contains the interaction of these inner and outer modes of being where God, soul, and world are always finely mingled, and in ways which are unique to the individual. This center is universal and particular, dynamic and essential, and is the only true self that can go forward Self’ing as God's mediator in the world.
(Unless otherwise noted, all quotes are from the excellent book The Radiance of Being: Dimensions of Cosmic Christianity by Stratford Caldecott.)