Shaun Gallagher states that it is possible to simplify various notions of the self into two categories; the 'minimal self' and the 'narrative self'.
[Gallagher, S. (2000). Philosophical conceptions of the self: implications for cognitive science. in Trends in Cognitive Sciences. 4(1).]
Narrative self is the coherent self that is constituted with a past and a future in the various stories that we and others tell about ourselves. It is a kind of ordinary self that we experience in our daily lives.
The minimal self is a self which is composed of minimal factors; all of the unessential features are stripped away. It is the consciousness of oneself as an immediate subject of experience, unextended in time. It is the 'I' who is experiencing 'now-here'.
The minimal self has the two aspects; the sense of agency and the sense of ownership. The ownership is the sense that it is my body that is moving, and the agency is the sense that I am the initiator or source of the action. They are indistinguishable in the normal experience of willed action. We have both senses at the same time.
But in the case of involuntary action (e.g. someone moved my hand), it is possible to distinguish between them. I have the sense that I am the one who is moving, but I don't have the sense that I am controlling the movement. That is, I have the sense of ownership but I don't have the sense of agency.
It would be interesting to research the impairments, alterations or lesions of these two basic senses in various body awareness disturbances; phantom limbs, asomatognosia, anosognosia, depersonalization, hemiplegia, etc. It will bring a light to the relation between the body and the self.