The way I sometimes describe it is that memory is essentially managed at compile time in Rust, whereas with a (tracing) GC it happens at runtime, and in C it's done manually by the programmer. This is a simplification, but it's both true that Rust is similar to C in that there isn't a runtime cost to memory managed and that it's similar to Java in that outside of specific APIs, you have strong guarantees about certain issues with memory not being possible because they're automatically handled by the language.