Racket was called PLT Scheme until 2010, and remains essentially a Scheme dialect. It diverged in part because of their disagreement with the minimalist direction of a large part of the Scheme community: PLT developers were heavily involved in the R6RS version of Scheme, which expanded the language's standard library considerably, but which much of the Scheme community rejected. Racket in part is the continuation of the R6RS "batteries included" philosophy, but removed from the politics of the Scheme revision process. (Another reason for the change was the emphasis on becoming a platform for language implementation that supports multiple languages, some increasingly divergent from Scheme, like Typed Racket.)

That's not the case at all.

The core of Racket, its syntax and basic constructs, is basically the small and elegant Scheme we all known and love. What set Racket apart is all of the additional features that was built around that tiny core (its own OO system, for example), as well as a huge standard library.

Racket is far closer to Scheme, from which it derives, than it is to Common Lisp -- which is why, before it was called "Racket" it was PLT Scheme. (And, in fact, the Racket tools include support for both r5rs and r6rs Scheme -- but not Common Lisp -- as well as the Racket language itself.)