Identity and Songs

I've been wondering about what makes a song the song that it is. That is, what are the necessary and sufficient conditions for being a particular song. Here's a clip from Ray Charles in 1968. He's performing a song called "Going Down Slow" (it's a pretty famous Blues standard).



And here's a clip from Eric Clapton singing "Going Down Slow." Notice that the titles of the songs are the same. The lyrics are very similar (though not identical) and there's clearly quite a bit in common between the two performances. But, at the same time, they're extremely different.



We might wonder whether Ray and Eric are playing the same song.

A natural answer is that they are playing different versions of the same song. They have their own interpretations of it, but it's just one song--"Going Down Slow." But this suggests that a number of things can be different between two performances and yet the two can be performances of the same song. For example, the chord progression between them can be different, the lyrics can be different, the tempo can be different, the instrumentation can be different, etc. Of course, they can't be too different--because then they wouldn't be performances of the same song. But where does one draw the line? In other words, what makes something a version of "Going Down Slow" as opposed to some other song? Interestingly, I've heard instrumental versions of "Going Down Slow," where there are no lyrics since no one is singing. It still seems right to say that the song performed was "Going Down Slow." So what do you think about these issues? What makes a song the song that it is?