C before C11 has no memory model. Rust doesn't have one but effectively it inherits the C++/C memory model, so there is actually no difference.
But the term could also be used more generally to include stuff like pointer provenance, Rust's "stacked borrows" etc. In that case, Rust is more complicated than C-as-specified. But C-in-reality is much more complicated, e.g. see https://www.open-std.org/jtc1/sc22/wg14/www/docs/n2263.htm