There are in fact, 4 edits of the video of which I know and have...
First is the main version or "edited" version. This is the one with no full frontal nudity.
Then there are 2 different edits of the X-Rated version. The second of which has alternative editing in the first half of the video. Some of the same shots are used but in a different order except for alternative shots of M shooting the pics with her in the infamous leather dominatrix bondage leotard, legs open, licking her riding crop. The video also opens with an 'advisory' message asking viewers "to call it a night" if they are offended by fantasies etc. This was clearly taken from a VHS tape and is perhaps the edit intended for the scrapped VHS release @AModSquadmentioned (maybe it's from a promo copy of the release?)
The fourth is a 4:31 edit from Promo Only. It's an edit of the main version so no nudity and could be the shortened version you are referring to @deathproof?