Remark: If selfhood is the same as personhood, then not all subjects are selves, because not all subjects are persons.
Here's how I put it, which I think works better -
In humans experiential content and the ways it manifests results in a Sense of being a discrete, unified, first person pov moving through space and time correlated to a specific body acting in an 'external' world. These properties enable us to have a mental model of our Self which we are aware of, can introspect, and give traits and agency to in the context of our overall model of the world, how it works and how we fit in.This individualised model of one's self (personhood if you like), will develop over time as we accrete history, introspect,expand our model, note particular traits, preferences and so on which amounts to a 'personality' we note has differences as well as similarities to others. We can also note ongoing traits and patterns which we can talk about as 'my identity', even though experiential states switch on and off and are always 'in the now'.
As regards ''Subject'', I'd be happy to call any critter which has any experiential state a Subject, whether or not she has a sense of self.
The point of the different labels is then to mark significant distinctions (probably inevitably blurry)
Subject - any entity which has any kind of experiential states.
Sense of self - see my definition.
Personhood - a more sophisticated, individualised model of self.
But I'm not that fussed about which labels we use, as long as they help us agree what we're talking about.
* When you write that "What constitutes such a thing…is essentially experiential", it's not clear to me whether this is an expression of reductive realism or nonreductive realism about subjects or selves.We know experiential states which amount to a sense of self are real. I've already said I think a sense of self is a feature of complex processes which require features like integration, a unified field, focus/attention/filtering and model building to be experientially coherent and therefore evolutionarily useful.
So yes I think a sense of being a self is a reducible sum of the processes of how experiential states manifest in humans and probably other complex animals. So I pretty much agree with this -
''According to reductive realism, the "empirical self" is the "total self", because there is no "pure ego" underlying and owning it, i.e. a distinct subject/object functioning as a substantial substratum of "the whole complex of contemporary and successive interrelated mental events which together constitute our mental history."
Here's a process-ontological expression of reductive realism, according to which selves aren't "substance-selves" but "process-selves" lacking a substantial substratum...We're not in a position to make such cut n dried distinctions between Substance-Selves and Process-Selves, without knowing the basis of the mind-body relationship. So far it looks like both are required, is the most we can assume based on what evidence we can observe.
So while I feel confident enough to posit that the self is reducible to its experiential parts based on evolution 'designing' a functionally coherent and useful way for experiential states to manifest, I don't have a path like that to understanding the underlying mind-body relationship. Experiential processes might or might not be the exact same thing as experiencing, but physical processes do seem necessary as far as we can tell. Framing the physical part as the Subject tho doesn't seem to capture the inherent experientialness of what being a Me means (as per my definition).