So, to lay it all out there:

In the beginning, there was multirust. This was a bash script, or rather, a set of them, I guess. It didn't really work on Windows, though, being a bash script.

Then came multirust-rs. We already have a programming language that we like to write that supports the platforms Rust supports: Rust! So, port multirust to Rust.

Then, it was decided that mutlirust-rs would be the right path to move forward generally, so a plan was formed to figure out just exactly how we'd want such a tool to truly work, rather than just copying what multirust did, and so this became rustup.