C isn't a big family of languages, it is very narrow family. Rust and Go are not in that family. A proper analogy requires some close dialectal ties, for instance:
ObjC - C beyond C++
What Rust and Go have in common is that they are Von Neumann model languages built around pushing word-sized quantities from memory through a CPU, like C, Pascal, Algol, Modula, ... thus:
Rust - "Von Neumann Model Algol-Like Blub Programming" beyond Go