Proton Stable
This is the default flavor of Proton that carries version number next to it, e.g. Proton 8.0-3. It's released after extensive QA testing and a public release candidate phase (example).
Sometimes upcoming Proton stable is released as Proton Next to facilitate more public testing ahead of a proper release.
Proton Experimental
This flavor is intended for public testing of experimental features. The games that are working only with Proton Experimental (as listed in the changelog) are tested for regressions prior to the release.
Proton Hotfix
It's a special version of Proton that contains targeted fixes for new, important games. It's used when there's no time to do a proper Stable or Experimental release. It's intended to be short lived and be phased out once the fix matures and is released as a part of one of the other flavors.
Proton Bleeding Edge
This is an automated and untested release of Proton that happens on Experimental's beta branch (find Proton Experimental in Steam's Library -> properties -> betas). It automatically picks up latest developemnt in dxvk, vkd3d-proton, dxvk-nvapi and Proton's wine.
It can eat your game prefix / saves. Use it at your own risk.