Yes, the kind of test case reduction that C-Reduce does is analogous to QuickCheck's shrinking. Some of C-Reduce's transformations are purely "on strings", e.g., "delete a physical line from the file", others are a bit more syntax-aware, e.g., "delete N tokens", and some actually build an AST using Clang and do some semantic transformations like "replace function parameter by global variable".

And yes, this is used alongside fuzzing, once a fuzzer (like Csmith from the same group as C-Reduce) has found a file that provokes a bug.

A reducer is not a fuzzer itself, although with some ingenuity it can be made to behave like a fuzzer in certain contexts: https://blog.regehr.org/archives/1284