Cork
A cork is a off axis spin that is leaned back, but so that the rider does not go inverted at any point. It is a popular trick, and many pro’s and amateurs do these very well.
Bio
A forward corking non-inverted spin. Note the lean the rider has forwards at about 360. Also, see CR Johnson in SM2, SM3 or Propaganda, he does them best.
D-spin
Set the same way a cork is, but is more leaned back. A d-spin is essentially any cork where you become inverted. In all of these videos note how the feet will go above the head. Evan Raps does these very well, also see Mike Douglas.
Flatspin
Flatspins are very close to rodeos. They are thrown almost the exact same, but the difference is that in a flatspin, the rider never gets completely inverted. Heres a way to think about it: A line extending through you from your head to your toes when you stand up. In a rodeo, this line ends up completely inverted at some point (although your feet can be somewhere else, like leaned back in a tail or a mute or something) while in a flatspin, this line never reaches true vertical. The line between what is a rodeo and a flatspin is understandably very blurry, especially when one considers tweaked grabs and such.