User blog comment:Lord Loss/Monster Hunter Frontier Season Forward 5/@comment-64.141.96.176-20121107000048/@comment-969093-20121116131138

Supremacy Odeibatorasu is basically a "more HC" version of the SR100 one. SR100 (HC) is the only non-supremacy kill quest, HR100 is repel-only. And the SR100/HR100 ones give different Gou Proofs.

xxx討伐の証 - Proof of Slaying (Toubatsu no Shou)

xxx撃退の証 - Proof of Repelling (Gekitai no Shou)

xxx = monster title

You need the repel proofs to make the base weapons and armors. I think you need the kill proofs for the upgraded weapons.