To me, the “Self” is — plain and simple — the part of us that keeps reliably showing up. It’s the part of us that we recognize as uniquely us, which sets us apart from everyone else, and feels familiar and comfortable on a deep, fundamental level. It’s who we are — and who we can expect ourselves to be in the course of everyday life.
Likewise, our Sense-Of-Self is a “felt sense” we have of the Self that is comfortable, confident, and put at ease by the predictability of how we express our Self. That feeling reinforces our understanding of who we are, when we experience our Self behaving predictably in various situations.