That's slightly misleading: there are two things: the environment and a base language.
Racket, as an environment, has compatibility due to its module/language approach to a bunch of languages. The older Scheme R5RS / R6RS are amongst those.
http://racket-lang.org
> Racket is a full-spectrum programming language. It goes beyond Lisp and Scheme with dialects that support objects, types, laziness, and more. Racket enables programmers to link components written in different dialects, and it empowers programmers to create new, project-specific dialects. Racket's libraries support applications from web servers and databases to GUIs and charts.
The main language under development aren't those, it's Racket:
http://racket-lang.org/new-name.html
> They draw you in with the promise of a simple and polite little Scheme, but soon you'll find yourself using modules, contracts, keyword arguments, classes, static types, and even curly braces.
> programmers can now simply say “Racket” to refer to the specific descendant of Scheme that powers PLT's languages and libraries.
There is a specific new language, a descendant of Scheme, in which this stuff is written, and that is called Racket.
This Racket language and its main libraries is documented here:
https://docs.racket-lang.org/reference/index.html
See also:
> Shriram Krishnamurthi
> Racket is Racket. It's its own language.
> I'm not quite sure what "Lisp family" really means, given that even Common Lispers and Schemers seem to argue more than agree (maybe because they're close family members?). Given that Sussman argues that Scheme is also a descendent of Algol, doesn't that put Racket in the Algol family as well? So Racket is both an Algol and a Lisp; would you change your posting to say “picks Algol to teach son programming”? In short, do these labels tell us anything useful at all?