I always mess this up, but here's something from memory: I believe there's ABI things that motivate stage 2. The compiler built in stage 0 has historically had special ifdefs to deal with "features that don't exist in the old snapshot" (we aggressively adopt our own features in the compiler and stdlib, because that's a great way to test them). This implies it can potentially emit binaries with a different ABI from the compilers built in stage 1 and 2. So the compiler that's output from stage 1 can actually have a different ABI from the binaries it produces.
Normally this wouldn't matter, but Rust also supports compiler plugins written in Rust. These link directly to the compiler that compiles them. With the stage 1 compiler's quirky ABI, the plugins it compiles might not be able to interact with it.
The stage 2 compiler, on the other hand, uses the same set of ifdefs that the stage 1 compiler has. So it was built by a compiler with the same output-ABI as itself, and so plugins have the same ABI.
So:
* snapshot: Built with snapshot ABI, produces snapshot ABI (snapshots are old stage2 compilers)
* stage0-output: built with snapshot ABI, emits stage0 ABI.
* stage1-output: built with stage0 ABI, emits not(stage0) ABI.
* stage2-output: built with not(stage0) ABI, emits not(stage0) ABI.