Rust can "just" be run; as in, the developer can create a binary and run that. Or you can compile from source without too much trouble with "cargo build".
Java is a bit more complex, and was even more complex in the past. You had to download Java (and on Windows, came with this annoying "Java updater" thing), and on Linux/BSD machines it couldn't "just" be installed via the package manager but had to manually download it from the Sun website (at some point Canonical got a special agreement with Sun to allow this though).
Later OpenJDK became mature enough to be used, which solved the entire problem, but that took quite a while.
This is why Java has traditionally not been huge in the open source world for writing applications.