Just like how Misty's are the opposites of Rodeo's, there are forward versions of corks and d-spins, but they're hard as fuck to do. A forward Cork = Bio, but most forward D-spins get lumped into the "Misty" category.
I've heard the term "Orbital" to describe the trick a few years ago, but as it takes me a great deal of analysis to detect the difference between a forward D-spin and a Misty, its not worth it. I'm fine with lumping them into the Misty category, dont see a need to change, it wont come down to a Misty and Forward D-spin going head to head in any big air finals anytime soon.