The B3 itself lets a player adjust the harmonics of the sound on the fly, shifting from a thick meaty sound to any number of thin reedy or subdued sounds with a single half-instinctual shove. The B3 is all over the place, from gospel to rock to radio plays. You’ll know it when you hear it even if you can’t name it.
And the Leslie. Oh, the Leslie. I heard it referred to as “a uniquely American design,” with a woofer aimed downward at a curved wooden wedge and a treble horn for the high frequencies, each piece rotating in opposite directions, throwing sound around a room and affecting the volume and frequencies of the organ in pleasing and interesting ways.
Lots of people have spent lots of time trying to recreate this sound in software, with varying degrees of success. My favorite example (real or simulated, I don’t know) is in Portishead’s “It’s a Fire”[0], since the organ is the main instrument and they put it through its paces: flipping the Leslie between its fast and slow modes while pulling the drawbars, and the tonal structure is wonderfully complex as well.
I think discovering the mechanics of these two things in tandem was part of what sparked my love of synthesizers and how they can be used to create and shift musical moods. The tools are a bit different but the fundamental idea is very similar.