Rust is solving the memory safety problem, Zig is solving the 'idiomatic interop with existing C coding patterns' problem. These couldn't be more different - C-like idiomatic code is generally antithetical to 'safe' modularity since it often relies on tacit global invariants for correct behavior.

Interestingly, Carbon is kinda trying to tackle both at the same time (though starting from C++ in their case) which is a bit of a challenge.