Such as Crush, Pierce, and Slash.
Mace: Abilities are augmented to deal Crush or Pierce Damage (A Focus on Crush)
Sword : Abilities are augmented to deal Slash or Pierce Damage (A Focus on Slash)
Axe: Abilities are augmented to deal Slash or Crush Damage (A Focus on Slash)
Dagger: Abilities are augmented to deal Pierce or Slash Damage (A focus on Pierce)
Crush Status Effect: Minor Fracture (Or Snare)
Slash Status Effect: Bleeding
Pierce Status Effect: Minor Vulnerability (Or target takes increased Critical Damage)
I know that there's already the Twin Blade and Blunt Passive, but I think these differences could be expanded upon.