If there is indeed no distinction between the two, which might very well be the case, you would still need to supply a logical argument as to why there is no distinction between the two. Philosophy isn't about positing grand-sounding statements without proof. It's about backing up such statements with valid logic.

Something like: Hello, I analysed 12 different ways in which people use the word "self", and came up with precise definitions for each of them so that there is no room for ambiguity or vagueness. Here I demonstrate that each and every one of them has exactly the same logical structure as, and is therefore reducible to, the phrase "the sense of self", a precise definition of which follows: blah blah blah. Therefore, I posit that "self" === "the sense of self".

Neuroscientists can show how certain biochemical processes cause members of homo sapiens to confuse the self with the sense of self, but error theory is not a positive demonstration. So I maintain that a healthy dose of philosophy is still required.

Also, just because you can't draw a line between two things doesn't mean that there's no distinction between them. Is abortion the same as murder just because foetal development is a continuous process with no sharp boundaries?