I don't think that's the parallel I would draw.
Rather, I think both Zig and Rust aim to serve the use cases C and C++ do, but Zig and Rust pick different points on the tradeoffs involving safety. Zig feels like a "better C", in the sense of bringing modern language features to C, but it chooses safer rather than safe. Rust supplies modern language features as well, and chooses to prioritize safe; sometimes that comes at the expense of other factors, such as productivity or compile time. I personally prefer the point on the spectrum that Rust chose, but I think Zig still offers improvements over C.