Ummm ... what ...
Spirits isn't physical, it doesn't use attack, accuracy, fSTR or any form of LCF. It's magical non-elemental as -MDT will reduce it's damage. Compared to Sang Blade which is Magical Darkness or Aeolian Edge which is Magical Wind.
Req is physical, it uses attack, accuracy, fSTR and LCF. It's physical non-elemental as -PDT will reduce it's damage. This is compared to Vorpal / CDC which is Physical Slashing or Evisceration which is Physical Piercing.
For crying out loud, Req STACKS with sneak attack, that kinda destroys your entire comment immediately.
There are two main types of damage, Physical and Magical, each has different subtypes.
Physical -> Slashing, Piercing, Blunt, Non-elemental
Magical -> Fire, Water, Thunder, Earth, Wind, Ice, Light, Dark, Non-elemental
Only thing that makes Req special is that monster physical resistances won't effect it. Slimes are Slashing -50% Blunt -75% Piercing -50% but magic +50%. Using Vorpal or CDC on them will have a -50% damage reduction, using Req will have no damage reduction. Using Sang or Aeolian Edge will have +50% damage bonus.
I don't know how to make it any simpler then this. This has all been tested prior to those WS's even being released into the live server. I've personally used Req vs various monsters on the test server to verify it's physical: non-elemental vs magical: non-elemental. Prime example is find a pot or eyeball, get it to use magic-shield then do Req. It will hit for full damage and completely ignore the magic shield effect.