The 'Band Mix' of WFTSC is a direct edit of the album version - same levels, effects and mix, just edited down. It's probably edited straight from the final, 2 track master of the album version - just listen to that horrible, mid-word edit just before the 1st chorus, where a little bit of the first verse is removed, and the line "she is lost forever more" becomes "she is lost forever shore", which makes no sense. A well-dodgy edit.
I'm assuming after the 'Band Mix' was edited, they handed the multi-track parts to Rich Costley for a bit more post-production (and a better edit of verse 1, where you actually here the last word of the verse properly) and a beefier mix to create his radio edit. A much better version.
I get the impression that the Band Mix was knocked up quickly, then someone decided it needed a better edit. Then the decision was made to bring out three seven inches and they needed an extra version of the title track, so the 'band mix' filled the slot. They'd've been better off just putting the regular album version on there, as it's not a great deal longer!
Andy