<pedantry> If each part is replaced in series, and the identity of the object remains the same after each step, then clearly the object remains the same. For humans identity is thus based on recognizing what you have seen before; it acknowledges mutable state. In this case, if you consider the brand as a mutable property of the object, then yes, the identity of PLT-Scheme and Racket are the same. </pedantry>
It looks to me like a lot of the core PLT guys were involved in the R6RS debacle, and didn't like what came out of the process so decided maybe they aren't quite an official "Scheme" anymore per R6RS. Oh the drama...
That said, I believe the have implemented scheme in Racket. I think PG implemented Arc in it too. It also comes with Algol-68 I think.