Rust's improvements over C don't just consist of memory safety. It also provides an excellent type system and the ability to statically check for concurrency bugs at a higher level than just memory safety, for instance.
None of these things (except maybe some of the concurrency stuff) are quite new to Rust. It's just that C is such an old language that stuff that other languages have been doing well for decades were not available to systems software.
None of these things (except maybe some of the concurrency stuff) are quite new to Rust. It's just that C is such an old language that stuff that other languages have been doing well for decades were not available to systems software.