It prevents data races, use-after-free, double-free, buffer overflow, invalid type punning, etc. You can still do all those things in unsafe code though, and you could in safe code if the unsafe code you depend on (including the kernel) behave/are programmed incorrectly. You can also have hardware issues and stochastic bit flips that Rust and SPARK can't deal with.

> So what does it mean for a program to be memory safe if it can still memory leak?

That it's not actually memory safe. Memory leaks are part of memory unsafety.