There's a strong similarity, all right. In both cases, the bullet-biters describe reality as we have every reason to believe it is, and ask the deniers how reality would be different if free will / personal continuity existed. The deniers don't have an answer, but they're very insistent about this feeling they have that this undefined free will or continuity thing exists.

Explaining this feeling could be interesting, but it has very little to do with the question of whether what the feeling is about, is real.