I believe Minefield is always the bleeding-edge (alpha) version. At the moment 4.0.12 is the stable beta, 4.0.13 is the Minefield alpha release, described by Mozilla as potentially buggy and slow.
Isn't Seamonkey also a rebranded FF? And isn't Minefield the bleeding-edge alpha? I'm confused.
It all starts with the netscape source release.
that source became Seamonkey; firefox was the result of turning seamonkey into a web browser rather then an integrated package (like netscape with all it's various bells and whistles). As far as I know Minefield is the 64-bit build of Firefox... anyway, Firefox and Seaweasel are certainly times of the same fork.
Quick google reveals that minefield also has 32-bit versions, and looks more like it is in fact a alpha of firefox, why they wouldn't just call it "Firefox Alpha Version whatever" is beyond me.
Also, why is it that they make 64-bit builds of prerelease code but ones it is in firefox they sort of push it aside and never actually build 64-bit? I mean, that just confuses people like me who like to pretend to know things.