I'm guessing you actually mean the seat pad, not the entire seat unit?
The seat pad on the BP seat unit, is lower at the back, to allow the overlap of the pillion seat pad.
You can put the Bip seat pad onto a mono seat, no problem, all mounting points "should" line up OK, but putting a mono seat on a Bip unit wouldn't work as the seat pad is higher, and you wouldn't be able to have the pillion pad on there.
Got to disagree on one point there guys. I have bought an SP seat unit and I tried to put the BP seat pad on that but it doesn't work. The holes are completely different so you can't put it on without drilling. You have to get an SP seat pad too.