Saying that a particular crate has a C API makes sense. Saying that Rust has a C API suggests that Rust has some equivalent to e.g. Python or Ruby's C APIs that

Saying that a particular crate has a C API makes sense. Saying that Rust has a C API suggests that Rust has some equivalent to e.g. Python or Ruby's C APIs that let you invoke arbitrary Rust code from C, which isn't true.