We used to call the Ron Allen versions 'Ollie Norths' and the now standard version 'one foot ollies' or 'ollie one foots.'. The difference is, Ron uses his back foot to get the board straight again whereas with one-foots, you have to use the front foot to kick the board into position before lofting your foot into orbit. The best one foots always have the slightly boned-look to the ollie (front pointing down)... Ron's version was really fun to do though. I might try and relearn them. There is also a version where you use your back hand to push the board back into position... aka the Ollie Scare-Walk ... ha ha.. H street days...
Once you learn the standard ollie one foot, please consider grabbing your tail...
Don't bother with Pierre Andre's back foot-one foot, that one is silly.