I wouldn't burden a lofty saddlepost with a lowly seat so why would I be dressing my ordinary seatpost with a highfalutin' saddle?
I've succumbed to calling those seats saddles at times, but all my bikes get seats; properly mounted on seatposts which are stuck in seatubes. (I grew up with saddles but we threw those on horses; not one of which had a seat anything.)