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.
Does that explain things well enough?